Chapter:

140+ Unit 1 Solved MCQs

in Discrete Structure (DS)

These multiple-choice questions (MCQs) are designed to enhance your knowledge and understanding in the following areas: Computer Science Engineering (CSE) .

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51.	In a class of 80 students , 50 students know English, 55 know french and 46 know german language. 37 students know english and french, 28 students know french and german, 7 students know none of the languages. Find out how many students know all the three languages?
A.	73
B.	72
C.	50
D.	54
Answer» A. 73

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52.	In above q.80 how many students exactly know 2 languages?
A.	52
B.	54
C.	60
D.	25
Answer» B. 54

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53.	In q. 80 how many students know exactly 1 language?
A.	54
B.	12
C.	7
D.	8
Answer» C. 7

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54.	A preposition is a statement that is either ture or false
A.	TRUE
B.	FALSE
C.	none
D.	both a and b
Answer» A. TRUE

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55.	A prepostition that is true under all circumstances is referred to as a ….
A.	Tautology
B.	Contradiction
C.	Negation
D.	Sentence
Answer» A. Tautology

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56.	A prepostition that is false under all circumstances is referred to as a ….
A.	Tautology
B.	Contradiction
C.	Negation
D.	Sentence
Answer» B. Contradiction

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57.	p→q is logically equivalent to ~p V q according to…
A.	Identity law
B.	Implication law
C.	associative law
D.	Absoption law
Answer» B. Implication law

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58.	A logical expression which consist of a product of elementary sum is caleed…..
A.	Disjunctive normal form
B.	Conjunctive normal form
C.	Normal form
D.	None
Answer» B. Conjunctive normal form

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59.	A logical expression which consist of a sum of product is caleed…..
A.	Disjunctive normal form
B.	Conjunctive normal form
C.	Normal form
D.	None
Answer» A. Disjunctive normal form

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60.	An assertion that contains one or more variable is called a….
A.	CNF
B.	DNF
C.	Predicates
D.	Quantifiers
Answer» C. Predicates

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61.	Determine the validity of argument given: s1: If I like mathematics then I will study. S2: Either I will study or I will fail. S: If I fail then I do not mlike mathematics.
A.	Valid
B.	Invalid
C.	Both a and b
D.	none
Answer» B. Invalid

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62.	p V ~(p٨q) is….
A.	Contradiction
B.	Tautology
C.	predicate
D.	None
Answer» B. Tautology

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63.	Determine the validity of the argument s1: If I stay up late at night , then I will be tired in the morning. S2: I stayed up last last night s: I am tired this morning.
A.	Valid
B.	Invalid
C.	Both a and b
D.	none
Answer» A. Valid

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64.	An argument is valid if, whenever the conclusion is true, thenthe premises are also true.
A.	TRUE
B.	FALSE
C.	both a and b
D.	none
Answer» B. FALSE

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65.	De Morgan's laaws are two examplesof rules of inference
A.	TRUE
B.	FALSE
C.	both a and b
D.	none
Answer» B. FALSE

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66.	In a club , all members participate either in tambola or the fete. 420 participate in the fete, 350 play tambola and 220 participate in both. How many members does the club have?
A.	250
B.	550
C.	120
D.	140
Answer» B. 550

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67.	dual of (p V q)٨ r is..
A.	p Vq
B.	(p٨q) Vr
C.	p ٨r
D.	(p Vq) Vr
Answer» B. (p٨q) Vr

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68.	It was found that in first year of computer science of 80 students 50 know Cobol, 55 know C, 46 know pascal. It was also known that 37 know C and cobol, 28 know C and pascal , 25 know pascal and cobol, 7 students know none of the languages. Find how many all the 3 languages?
A.	10
B.	12
C.	35
D.	9
Answer» B. 12

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69.	In above q.97 How many know exactly 2 languages?
A.	54
B.	16
C.	10
D.	35
Answer» A. 54

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70.	In q.97. How many know exactly 1 language?
A.	6
B.	16
C.	7
D.	10
Answer» C. 7

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71.	In the class of 55 students the number ofstudying different subjects are as given below: Maths 23, Physics 24, chemistry 19, maths+physics 12, maths+chemistry 9, Physics +chemistry 7, all three subjects 4. Find the number of students who have taken atleast 1 subject?
A.	22
B.	45
C.	42
D.	14
Answer» C. 42

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72.	[~ q ^ (p→q)]→~ p is,
A.	Satisfiable
B.	tautology
C.	unsatisfiable
D.	contradiction
Answer» B. tautology

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73.	If P and Q stands for the statement P : It is hot Q : It is humid, then what does the following mean? P Ù (~ Q):
A.	It is got and it is humid
B.	It is hot and it is not humid
C.	it is not hot and it is humid
D.	none
Answer» B. It is hot and it is not humid

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74.	In a survey of 85 people it is found that 31 like to drink milk, 43 like coffee and 39 like tea.Also 13 like both milk and tea, 15 like milk and coffee, 20 like tea and coffee and 12 like none of the three drinks. Find the number of people who like all the three drinks.
A.	10
B.	9
C.	8
D.	7
Answer» C. 8

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75.	The statement ( p^q) → p is a
A.	absurdity
B.	contadiction
C.	tautology
D.	none
Answer» C. tautology

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76.	Let p be “He is tall” and let q “He is handsome”. Then the statement “It is false that he is short or handsome” is:
A.	p ^ q
B.	~ (~ p ^q)
C.	p^ ~ q
D.	~ p ^q
Answer» B. ~ (~ p ^q)

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77.	Let P(S) denotes the powerset of set S. Which of the following is always true?
A.	P(P(S)) = P(S)
B.	P(S) IS = P(S)
C.	P(S) I P(P(S)) = {ø}
D.	S € P(S)
Answer» D. S € P(S)

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78.	Which of the following proposition is a tautology?
A.	(p v q)→p
B.	p v (q→p)
C.	p v (p→q)
D.	p→(p→q)
Answer» C. p v (p→q)

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79.	Which of the following statement is the negation of the statement “4 is even or -5 is negative”?
A.	4 is odd and -5 is not negative
B.	4 is even or -5 is not negative
C.	4 is odd or -5 is not negative
D.	4 is even and -5 is not negative
Answer» A. 4 is odd and -5 is not negative

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80.	Which one is the contrapositive of q → p ?
A.	p → q
B.	~p →~q
C.	~q→~p
D.	None
Answer» B. ~p →~q

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81.	Check the validity of the following argument :- “If the labour market is perfect then the wages of all persons in a particular employment will be equal. But it is always the case that wages for such persons are not equal therefore the labour market is not perfect.”
A.	Invalid
B.	Valid
C.	Both a and b
D.	None
Answer» B. Valid

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82.	∃ is used in predicate calculus to indicate that a predicate is true for all members of a specified set.
A.	TRUE
B.	FALSE
C.	Both a and b
D.	None
Answer» A. TRUE

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83.	∀ is used in predicate calculus to indicate that a predicate is true for at least one member of a specified set.
A.	TRUE
B.	FALSE
C.	Both a and b
D.	None
Answer» A. TRUE

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84.	“If the sky is cloudy then it will rain and it will not rain”
A.	absurdity
B.	contadiction
C.	tautology
D.	none
Answer» C. tautology

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85.	Represent statement into predicate calculus forms : "Not all birds can fly". Let us assume the following predicates bird(x): “x is bird” fly(x): “x can fly”.
A.	∃x bird(x) V fly(x)
B.	∃x bird(x) ^ ~ fly(x)
C.	∃x bird(x) ^ fly(x)
D.	None
Answer» B. ∃x bird(x) ^ ~ fly(x)

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86.	Represent statement into predicate calculus forms : "If x is a man, then x is a giant." Let us assume the following predicates man(x): “x is Man” giant(x): “x is giant”.
A.	∀ (man(x)→ ~giant(x))
B.	∀ man(x)→ giant(x)
C.	∀ (man(x)→ giant(x))
D.	None
Answer» C. ∀ (man(x)→ giant(x))

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87.	Represent statement into predicate calculus forms : "Some men are not giants." Let us assume the following predicates man(x): “x is Man” giant(x): “x is giant”.
A.	∃x man(x) ^ giant(x)
B.	∃x man(x) ^ ~ giant(x)
C.	∃x man(x) V ~ giant(x)
D.	None
Answer» B. ∃x man(x) ^ ~ giant(x)

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88.	Represent statement into predicate calculus forms : There is a student who likes mathematics but not history. Let us assume the following predicates student(x): “x is student.” likes(x, y): “x likes y”. and ~likes(x, y) “x does not like y”.
A.	∃x [student(x) ^ likes(x, mathematics) ^~ likes(x, history)]Q.
B.	∃x [student(x) ^Vlikes(x, mathematics) V~ likes(x, history)]Q.
C.	∃x [student(x) ^ ~likes(x, mathematics) ^likes(x, history)]Q.
D.	None
Answer» A. ∃x [student(x) ^ likes(x, mathematics) ^~ likes(x, history)]Q.

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89.	AUB = (A− B)U(B−A)U(AпB).
A.	FALSE
B.	TRUE
C.	Both a and b
D.	None
Answer» B. TRUE

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90.	[(PVQ)^(P→R)^(Q→S)] → (SVR). Is a….
A.	absurdity
B.	contadiction
C.	tautology
D.	none
Answer» C. tautology

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91.	~(x vy) = ~x ^ ~y
A.	FALSE
B.	TRUE
C.	Both a and b
D.	None
Answer» B. TRUE

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92.	(x ^ y)’ = x’ V y’
A.	FALSE
B.	TRUE
C.	Both a and b
D.	None
Answer» B. TRUE

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93.	Test the validity of argument:“If it rains tomorrow, I will carry my umbrella, if its cloth is mended. It will rain tomorrow and the cloth will not be mended. Therefore I will not carry my umbrella”
A.	Invalid
B.	Valid
C.	Both a and b
D.	None
Answer» B. Valid

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94.	In a group of athletic teams in a certain institute, 21 are in the basket ball team, 26 in the hockey team, 29 in the foot ball team. If 14 play hockey and basketball, 12 play foot ball and basket ball, 15 play hockey and foot ball, 8 play all the three games. (i) How many players are there in all?
A.	78
B.	98
C.	23
D.	43
Answer» D. 43

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95.	In above Q.123 (ii) How many play only foot ball?
A.	10
B.	8
C.	9
D.	4
Answer» A. 10

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96.	(p ↔ q) ↔ r = p ↔ (q ↔ r)
A.	absurdity
B.	contadiction
C.	tautology
D.	none
Answer» C. tautology

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97.	Write the negation in good english sentence : "Jack did not eat fat, but he did eat broccoli."
A.	If Jack eat and broccoli then he did ate fat.
B.	If Jack did not eat broccoli then he did ate fat.
C.	If Jack did not eat broccoli or he did ate fat.
D.	If Jack did not eat broccoli then he did not ate fat.
Answer» B. If Jack did not eat broccoli then he did ate fat.

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98.	Write the negation in good english sentence : The weather is bad and I will not go to work.
A.	The weather is not bad or I will go to work.
B.	The weather is good or I will go to work.
C.	The weather is not bad or I will not go to work.
D.	None
Answer» A. The weather is not bad or I will go to work.

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99.	Write the negation in good english sentence : Mary lost her lamb or the wolf ate the lamb.
A.	Mary did loss her lamb and the wolf eat the lamb.
B.	Mary did loss her lamb and the wolf did not eat the lamb.
C.	Mary did not loss her lamb and the wolf did not eat the lamb.
D.	None
Answer» C. Mary did not loss her lamb and the wolf did not eat the lamb.

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100.	Write the negation in good english sentence : I will not win the game or I will not enter the contest.
A.	I will not win the game and I will enter the contest.
B.	I will win the game and I will enter the contest.
C.	I will win the game and I will not enter the contest.
D.	None
Answer» B. I will win the game and I will enter the contest.

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140+ Unit 1 Solved MCQs

In a class of 80 students , 50 students know English, 55 know french and 46 know german language. 37 students know english and french, 28 students know french and german, 7 students know none of the languages. Find out how many students know all the three languages?

In above q.80 how many students exactly know 2 languages?

In q. 80 how many students know exactly 1 language?

A preposition is a statement that is either ture or false

A prepostition that is true under all circumstances is referred to as a ….

A prepostition that is false under all circumstances is referred to as a ….

p→q is logically equivalent to ~p V q according to…

A logical expression which consist of a product of elementary sum is caleed…..

A logical expression which consist of a sum of product is caleed…..

An assertion that contains one or more variable is called a….

Determine the validity of argument given: s1: If I like mathematics then I will study. S2: Either I will study or I will fail. S: If I fail then I do not mlike mathematics.

p V ~(p٨q) is….

Determine the validity of the argument s1: If I stay up late at night , then I will be tired in the morning. S2: I stayed up last last night s: I am tired this morning.

An argument is valid if, whenever the conclusion is true, thenthe premises are also true.

De Morgan's laaws are two examplesof rules of inference

In a club , all members participate either in tambola or the fete. 420 participate in the fete, 350 play tambola and 220 participate in both. How many members does the club have?

dual of (p V q)٨ r is..

It was found that in first year of computer science of 80 students 50 know Cobol, 55 know C, 46 know pascal. It was also known that 37 know C and cobol, 28 know C and pascal , 25 know pascal and cobol, 7 students know none of the languages. Find how many all the 3 languages?

In above q.97 How many know exactly 2 languages?

In q.97. How many know exactly 1 language?

In the class of 55 students the number ofstudying different subjects are as given below: Maths 23, Physics 24, chemistry 19, maths+physics 12, maths+chemistry 9, Physics +chemistry 7, all three subjects 4. Find the number of students who have taken atleast 1 subject?

[~ q ^ (p→q)]→~ p is,

If P and Q stands for the statement P : It is hot Q : It is humid, then what does the following mean? P Ù (~ Q):

In a survey of 85 people it is found that 31 like to drink milk, 43 like coffee and 39 like tea.Also 13 like both milk and tea, 15 like milk and coffee, 20 like tea and coffee and 12 like none of the three drinks. Find the number of people who like all the three drinks.

The statement ( p^q) → p is a

Let p be “He is tall” and let q “He is handsome”. Then the statement “It is false that he is short or handsome” is:

Let P(S) denotes the powerset of set S. Which of the following is always true?

Which of the following proposition is a tautology?

Which of the following statement is the negation of the statement “4 is even or -5 is negative”?

Which one is the contrapositive of q → p ?

Check the validity of the following argument :- “If the labour market is perfect then the wages of all persons in a particular employment will be equal. But it is always the case that wages for such persons are not equal therefore the labour market is not perfect.”

∃ is used in predicate calculus to indicate that a predicate is true for all members of a specified set.

∀ is used in predicate calculus to indicate that a predicate is true for at least one member of a specified set.

“If the sky is cloudy then it will rain and it will not rain”

Represent statement into predicate calculus forms : "Not all birds can fly". Let us assume the following predicates bird(x): “x is bird” fly(x): “x can fly”.

Represent statement into predicate calculus forms : "If x is a man, then x is a giant." Let us assume the following predicates man(x): “x is Man” giant(x): “x is giant”.

Represent statement into predicate calculus forms : "Some men are not giants." Let us assume the following predicates man(x): “x is Man” giant(x): “x is giant”.

Represent statement into predicate calculus forms : There is a student who likes mathematics but not history. Let us assume the following predicates student(x): “x is student.” likes(x, y): “x likes y”. and ~likes(x, y) “x does not like y”.

AUB = (A− B)U(B−A)U(AпB).

[(PVQ)^(P→R)^(Q→S)] → (SVR). Is a….

~(x vy) = ~x ^ ~y

(x ^ y)’ = x’ V y’

Test the validity of argument:“If it rains tomorrow, I will carry my umbrella, if its cloth is mended. It will rain tomorrow and the cloth will not be mended. Therefore I will not carry my umbrella”

In a group of athletic teams in a certain institute, 21 are in the basket ball team, 26 in the hockey team, 29 in the foot ball team. If 14 play hockey and basketball, 12 play foot ball and basket ball, 15 play hockey and foot ball, 8 play all the three games. (i) How many players are there in all?

In above Q.123 (ii) How many play only foot ball?

(p ↔ q) ↔ r = p ↔ (q ↔ r)

Write the negation in good english sentence : "Jack did not eat fat, but he did eat broccoli."

Write the negation in good english sentence : The weather is bad and I will not go to work.

Write the negation in good english sentence : Mary lost her lamb or the wolf ate the lamb.

Write the negation in good english sentence : I will not win the game or I will not enter the contest.

If P and Q stands for the statement P : It is hot
Q : It is humid,
then what does the following mean? P Ù (~ Q):

Check the validity of the following argument :- “If the labour market is perfect then the wages of all persons in a particular employment
will be equal. But it is always the case that wages for such persons are not equal
therefore the labour market is not perfect.”

∃ is used in predicate calculus
to indicate that a predicate is true for all members of a
specified set.

∀ is used in predicate calculus
to indicate that a predicate is true for at least one
member of a specified set.