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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101.	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.	9
B.	8
C.	10
D.	11
Answer» B. 8

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102.	Find the negation of the proposition: “Michael’s PC runs Linux”
A.	“It is not the case that Michael’s PC runs Linux.”
B.	“Michael’s PC does not run Linux.”
C.	Both a and b
D.	Only a
Answer» C. Both a and b

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103.	A proof that begins by asserting a claim and proceeds to show that the claim cannot be true is by
A.	Induction
B.	Contradiction
C.	prevarication
D.	construction
Answer» B. Contradiction

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104.	A proof that proceeds by showing the existence of something desired is by
A.	Induction
B.	Contradiction
C.	prevarication
D.	construction
Answer» A. Induction

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105.	Proofs by contradiction
A.	dismiss certain rules of logic
B.	misrepresent facts
C.	start by assuming the opposite of what is to be proven
D.	end by rejecting what is to be proven
Answer» C. start by assuming the opposite of what is to be proven

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106.	Induction is a
A.	algorithm
B.	program
C.	Proof
D.	Proof method
Answer» D. Proof method

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107.	^ denotes
A.	union
B.	AND
C.	set membership
D.	negation
Answer» B. AND

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108.	~ denotes
A.	union
B.	AND
C.	set membership
D.	negation
Answer» D. negation

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109.	Quantifiers variables
A.	Negate
B.	Change
C.	give values to
D.	bind
Answer» C. give values to

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110.	A validity-maintaining procedure for deriving sentences in logic from other sentences is
A.	Proof
B.	Theorem
C.	Inference rule
D.	inference chain
Answer» C. Inference rule

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111.	Inference rules maintain
A.	completeness
B.	validity
C.	satisfiablity
D.	logic
Answer» B. validity

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112.	A validity-maintaining procedure for deriving sentences in logic from other sentences is a
A.	Proof
B.	Theorem
C.	Inference rule
D.	inference chain
Answer» C. Inference rule

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113.	If A and B be sets and AC and Bc denote the complements of the sets A and B, then set (A — B) ∪ (B — A) ∪ (A ∩ B) is equal to
A.	Ac ∪ Bc
B.	Ac ∩ Bc
C.	A ∪ B
D.	A ∩ B
Answer» C. A ∪ B

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114.	Number of proper subsets of a set of order three
A.	3
B.	6
C.	8
D.	9
Answer» B. 6

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115.	If A be a finite set of size n, then number of elements in the power set of A x A is
A.	22^n
B.	2n^2
C.	(2n)2
D.	none
Answer» B. 2n^2

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116.	Which of the following set (s) are empty ?
A.	{x : x = x}
B.	{x : x ≠ x}
C.	{x : x = x2}
D.	{x : x ≠ x2}
Answer» B. {x : x ≠ x}

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117.	n a Venn diagram , the overlap between two circles represents:
A.	the union of two sets
B.	the intersection of two sets
C.	the elements that are in either of two sets
D.	the difference between the number of elements in two sets
Answer» B. the intersection of two sets

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118.	Which of these subsets are equal: A = {r.t.s} B = {s,t,r,s} C = {t,s,t,r} D = {s,r,s,t}
A.	A and B
B.	A and C
C.	B and D
D.	all are equal
Answer» D. all are equal

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119.	Determine the total number of subsets of the following set: {h,i, j, k, l, m, n}
A.	128
B.	64
C.	32
D.	14
Answer» A. 128

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120.	If B is a Boolean Algebra, then which of the following is true
A.	B is a finite but not complemented lattice
B.	B is a finite, complemented and distributive lattice
C.	B is a finite, distributive but not complemente d lattice
D.	B is not distributive lattice
Answer» B. B is a finite, complemented and distributive lattice

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121.	The statement ( p^q) _ p is a
A.	Contingency
B.	contradiction
C.	tautology
D.	None
Answer» C. tautology

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122.	1. Let m = “Juan is a math major,” c = “Juan is a computer science major,” g = “Juan’s girlfriend is a literature major,” h = “Juan’s girlfriend has read Hamlet,” and t = “Juan’s girlfriend has read The Tempest.” Which of the following expresses the statement “Juan is a computer science major and a math major, but his girlfriend is a literature major who hasn’t read both The Tempest and Hamlet.”
A.	c ∧ m ∧ (g ∨ (∼h ∨ ∼t))
B.	c ∧ m ∧ g ∧ (∼h ∧ ∼t)
C.	c ∧ m ∧ g ∧ (∼h ∨ ∼t)
D.	c ∧ m ∧ (g ∨ (∼h ∧ ∼t))
Answer» C. c ∧ m ∧ g ∧ (∼h ∨ ∼t)

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123.	The truth table for (p ∨ q) ∨ (p ∧ r) is the same as the truth table for
A.	(p ∨ q) ∧ (p ∨ r)
B.	(p ∨ q) ∧ r
C.	(p ∨ q) ∧ (p ∧ r)
D.	p V q
Answer» D. p V q

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124.	Consider the statement, “Either −2 ≤ x ≤ −1 or 1 ≤ x ≤ 2.” The negation of this statement is
A.	x < −2 or 2 < x or −1 < x < 1
B.	(x < −2 or 2 < x
C.	−1 < x < 1
D.	x ≤ −2 or 2 ≤ x or −1 < x < 1
Answer» A. x < −2 or 2 < x or −1 < x < 1

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125.	Which of the following statements is FALSE:
A.	(P ∧ Q) ∨ (∼P ∧ Q) ∨ (P ∧ ∼Q) is equal to ∼Q ∧ ∼P
B.	(P ∧ Q) ∨ (∼P ∧ Q) ∨ (P ∧ ∼Q) is equal to Q ∨ P
C.	(P ∧ Q) ∨ (∼P ∧ Q) ∨ (P ∧ ∼Q) is equal to Q ∨ (P ∧ ∼Q)
D.	(P ∧ Q) ∨ (∼P ∧ Q) ∨ (P ∧ ∼Q) is equal to [(P ∨ ∼P) ∧ Q] ∨ (P ∧ ∼Q)
Answer» A. (P ∧ Q) ∨ (∼P ∧ Q) ∨ (P ∧ ∼Q) is equal to ∼Q ∧ ∼P

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126.	anya is older than Eric. Cliff is older than Tanya. Eric is older than Cliff. If the first two statements are true, the third statement is
A.	TRUE
B.	FALSE
C.	Both
D.	None
Answer» B. FALSE

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127.	Blueberries cost more than strawberries. Blueberries cost less than raspberries.Raspberries cost more than both strawberries and blueberries. If the first two statements are true, the third statement is
A.	TRUE
B.	FALSE
C.	Both
D.	None
Answer» A. TRUE

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128.	All the trees in the park are flowering trees. Some of the trees in the park are dogwoods. All dogwoods in the park are flowering trees. If the first two statements are true, the third statement is
A.	TRUE
B.	FALSE
C.	Both
D.	None
Answer» A. TRUE

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129.	Mara runs faster than Gail.Lily runs faster than Mara.Gail runs faster than Lily.If the first two statements are true, the third statement is
A.	TRUE
B.	FALSE
C.	Both
D.	None
Answer» B. FALSE

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130.	Apartments in the Riverdale Manor cost less than apartments in The Gaslight Commons.Apartments in the Livingston Gate cost more than apartments in the The Gaslight Commons.Of the three apartment buildings, the Livingston Gate costs the most.If the first two statements are true, the third statement is
A.	TRUE
B.	FALSE
C.	Both
D.	None
Answer» A. TRUE

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131.	The power set of the set {ϕ} is
A.	{ϕ}
B.	{ϕ, {ϕ}}
C.	{0}
D.	None
Answer» B. {ϕ, {ϕ}}

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132.	Fact 1:All dogs like to run.Fact 2:Some dogs like to swim.Fact 3:Some dogs look like their masters.If the first three statements are facts, which of the following statements must also be a fact? I:All dogs who like to swim look like their masters. II:Dogs who like to swim also like to run.III:Dogs who like to run do not look like their masters.
A.	I only
B.	II only
C.	III only
D.	All
Answer» B. II only

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133.	Fact 1: Jessica has four children Fact 2: Two of the children have blue eyes and two of the children have brown eyes. Fact 3: Half of the children are girls. If the first three statements are facts, which of the following statements must also be a fact? I: At least one girl has blue eyes. II: Two of the children are boys. III: The boys have brown eyes.
A.	I only
B.	II only
C.	III only
D.	All
Answer» B. II only

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134.	Fact 1: All drink mixes are beverages. Fact 2: All beverages are drinkable. Fact 3: Some beverages are red. If the first three statements are facts, which of the following statements must also be a fact? I: Some drink mixes are red. II: All beverages are drink mixes. III: All red drink mixes are drinkable.
A.	I only
B.	II only
C.	III only
D.	All
Answer» C. III only

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135.	Fact 1: All chickens are birds. Fact 2: Some chickens are hens. Fact 3: Female birds lay eggs. If the first three statements are facts, which of the following statements must also be a fact? I: All birds lay eggs. II: Some Hens are birds. III: Some chickens are not hens.
A.	I only
B.	II only
C.	II and III only
D.	All
Answer» C. II and III only

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136.	100 sportsmen were asked whether they play which game: Cricket, hockey,Football. The results were : 45 play cricket, 38 play hockey, 21 play football, 18 play cricket and hockey, 9 play cricket and football, 4 play football and hockey and 23 play none of these. Determine the number of sportsmen who play exactly 1game
A.	54
B.	84
C.	56
D.	78
Answer» A. 54

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137.	In above Ex. 196 how many players play exactly 2 of the games?
A.	29
B.	79
C.	19
D.	39
Answer» C. 19

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138.	A theory of sets was firstly introduced by….
A.	Tim berners lee
B.	Franklin
C.	G.Canter
D.	c.panther
Answer» C. G.Canter

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139.	the inventor of set defined set as
A.	collection od distinct objects
B.	collection of memebers
C.	simple as collection of objects
D.	simply as collection of alphabets
Answer» C. simple as collection of objects

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140.	class, groups , collection are synonyms of the term set.
A.	TRUE
B.	FALSE
C.	both a and b
D.	none
Answer» A. TRUE

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140+ Unit 1 Solved MCQs

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.

Find the negation of the proposition: “Michael’s PC runs Linux”

A proof that begins by asserting a claim and proceeds to show that the claim cannot be true is by

A proof that proceeds by showing the existence of something desired is by

Proofs by contradiction

Induction is a

^ denotes

~ denotes

Quantifiers variables

A validity-maintaining procedure for deriving sentences in logic from other sentences is

Inference rules maintain

A validity-maintaining procedure for deriving sentences in logic from other sentences is a

If A and B be sets and AC and Bc denote the complements of the sets A and B, then set (A — B) ∪ (B — A) ∪ (A ∩ B) is equal to

Number of proper subsets of a set of order three

If A be a finite set of size n, then number of elements in the power set of A x A is

Which of the following set (s) are empty ?

n a Venn diagram , the overlap between two circles represents:

Which of these subsets are equal: A = {r.t.s} B = {s,t,r,s} C = {t,s,t,r} D = {s,r,s,t}

Determine the total number of subsets of the following set: {h,i, j, k, l, m, n}

If B is a Boolean Algebra, then which of the following is true

The statement ( p^q) _ p is a

The truth table for (p ∨ q) ∨ (p ∧ r) is the same as the truth table for

Consider the statement, “Either −2 ≤ x ≤ −1 or 1 ≤ x ≤ 2.” The negation of this statement is

Which of the following statements is FALSE:

anya is older than Eric. Cliff is older than Tanya. Eric is older than Cliff. If the first two statements are true, the third statement is

Blueberries cost more than strawberries. Blueberries cost less than raspberries.Raspberries cost more than both strawberries and blueberries. If the first two statements are true, the third statement is

All the trees in the park are flowering trees. Some of the trees in the park are dogwoods. All dogwoods in the park are flowering trees. If the first two statements are true, the third statement is

Mara runs faster than Gail.Lily runs faster than Mara.Gail runs faster than Lily.If the first two statements are true, the third statement is

The power set of the set {ϕ} is

Fact 1: All chickens are birds. Fact 2: Some chickens are hens. Fact 3: Female birds lay eggs. If the first three statements are facts, which of the following statements must also be a fact? I: All birds lay eggs. II: Some Hens are birds. III: Some chickens are not hens.

In above Ex. 196 how many players play exactly 2 of the games?

A theory of sets was firstly introduced by….

the inventor of set defined set as

class, groups , collection are synonyms of the term set.

Fact 1: All chickens are birds. Fact 2: Some chickens are hens. Fact 3: Female birds lay eggs.
If the first three statements are facts, which of the following statements must also be a fact?
I: All birds lay eggs.
II: Some Hens are birds.
III: Some chickens are not hens.