Q.1 Which of the following is a subset of every set?
Empty set
Universal set
Singleton set
Power set
Explanation - The empty set (∅) is a subset of every set by definition.
Correct answer is: Empty set
Q.2 If A = {1, 2, 3} and B = {3, 4, 5}, what is A ∪ B?
{1, 2}
{1, 2, 3, 4, 5}
{3}
{1, 2, 4, 5}
Explanation - The union of two sets includes all elements present in either set.
Correct answer is: {1, 2, 3, 4, 5}
Q.3 Which law states that A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)?
Distributive law
Associative law
Commutative law
De Morgan's law
Explanation - The distributive law shows how union distributes over intersection.
Correct answer is: Distributive law
Q.4 What is the complement of the universal set U?
Empty set
U itself
Undefined
Singleton set
Explanation - The complement of the universal set contains all elements not in U, which is ∅.
Correct answer is: Empty set
Q.5 If P and Q are propositions, which of the following is a tautology?
P ∧ ¬P
P ∨ ¬P
P ∧ Q
¬P ∧ ¬Q
Explanation - P ∨ ¬P is always true regardless of the truth value of P.
Correct answer is: P ∨ ¬P
Q.6 Which of the following is true for sets A and B if A ∩ B = ∅?
A and B are equal
A and B are disjoint
A is a subset of B
B is a subset of A
Explanation - Two sets with no elements in common are called disjoint sets.
Correct answer is: A and B are disjoint
Q.7 The number of subsets of a set with n elements is:
n
2n
2^n
n!
Explanation - A set with n elements has 2^n subsets, including the empty set and itself.
Correct answer is: 2^n
Q.8 Which of the following represents the intersection of sets A and B?
A ∪ B
A ∩ B
A − B
B − A
Explanation - Intersection includes only elements common to both sets.
Correct answer is: A ∩ B
Q.9 If A ⊆ B and B ⊆ C, then which of the following is true?
A ⊆ C
C ⊆ A
A = B
B = C
Explanation - Subset relation is transitive: if A is subset of B and B of C, then A is subset of C.
Correct answer is: A ⊆ C
Q.10 Which of the following is an example of a proposition?
x + 2
2 + 2 = 4
Run!
Who are you?
Explanation - A proposition is a declarative statement that is either true or false.
Correct answer is: 2 + 2 = 4
Q.11 De Morgan's law states that ¬(A ∩ B) equals:
¬A ∩ ¬B
¬A ∪ ¬B
A ∪ B
A ∩ B
Explanation - De Morgan's laws relate complements of unions and intersections.
Correct answer is: ¬A ∪ ¬B
Q.12 If U = {1,2,3,4,5}, A = {1,2}, B = {2,3}, find A − B.
{1}
{2}
{3}
{1,3}
Explanation - A − B contains elements in A but not in B.
Correct answer is: {1}
Q.13 The statement 'If it rains, then the ground is wet' is an example of:
Conjunction
Implication
Disjunction
Negation
Explanation - This is a conditional statement of the form 'If P then Q'.
Correct answer is: Implication
Q.14 Which of the following sets is a proper subset of {1,2,3}?
{1,2,3}
{1,2}
{1,2,3,4}
{ }
Explanation - A proper subset contains some but not all elements of the set.
Correct answer is: {1,2}
Q.15 The converse of 'If P, then Q' is:
If Q, then P
If not P, then not Q
If not Q, then not P
P ∧ Q
Explanation - The converse of a conditional statement swaps the hypothesis and conclusion.
Correct answer is: If Q, then P
Q.16 Which of the following is true for A ∪ A?
A
∅
U
2A
Explanation - Union of a set with itself gives the set itself.
Correct answer is: A
Q.17 If P: 'It is raining' and Q: 'I carry an umbrella', which represents ¬P ∨ Q?
If it rains, I carry an umbrella
If it does not rain or I carry an umbrella
It rains and I do not carry an umbrella
I carry an umbrella only if it rains
Explanation - ¬P ∨ Q means either P is false (no rain) or Q is true (umbrella).
Correct answer is: If it does not rain or I carry an umbrella
Q.18 Which of the following is a contradiction?
P ∧ ¬P
P ∨ ¬P
P → P
P ∨ Q
Explanation - P ∧ ¬P is always false regardless of P.
Correct answer is: P ∧ ¬P
Q.19 The power set of {a, b} is:
{a, b}
{∅, {a}, {b}, {a,b}}
{{a},{b}}
{∅}
Explanation - Power set contains all subsets including empty set and the set itself.
Correct answer is: {∅, {a}, {b}, {a,b}}
Q.20 Which of the following is true for sets A and B if A ⊆ B?
A ∩ B = B
A ∪ B = B
A − B = A
B − A = ∅
Explanation - Union of a subset with its superset is the superset.
Correct answer is: A ∪ B = B
Q.21 Which statement is logically equivalent to ¬(P ∨ Q)?
¬P ∧ ¬Q
¬P ∨ ¬Q
P ∧ Q
P ∨ Q
Explanation - This is De Morgan's law.
Correct answer is: ¬P ∧ ¬Q
Q.22 If A = {1, 2, 3} and B = {2, 3, 4}, what is A ∩ B?
{1,4}
{2,3}
{1,2,3,4}
{ }
Explanation - Intersection includes elements common to both sets.
Correct answer is: {2,3}
Q.23 Which logical operator represents 'and'?
∧
∨
¬
→
Explanation - The symbol ∧ represents conjunction (logical AND).
Correct answer is: ∧
Q.24 Which of the following is true for the empty set ∅?
∅ ∪ A = A
∅ ∩ A = A
∅ ⊆ A = false
∅ ∩ A = A
Explanation - Union with the empty set does not change the set.
Correct answer is: ∅ ∪ A = A