\[
\textbf{MCQs on Mathematical Logic and Set Theory with Answers}
\]
\[
\textbf{Q1: In propositional logic, a tautology is:}
\]
\[
\text{(A) A statement that is always true} \quad
\text{(B) A statement that is always false} \quad
\text{(C) A statement that is sometimes true and sometimes false} \quad
\text{(D) None of these}
\]
\[
\textbf{Answer: (A) A statement that is always true}
\]
\[
\textbf{Q2: The contrapositive of the statement “If P, then Q” is:}
\]
\[
\text{(A) If Q, then P} \quad
\text{(B) If not Q, then not P} \quad
\text{(C) If not P, then not Q} \quad
\text{(D) None of these}
\]
\[
\textbf{Answer: (B) If not Q, then not P}
\]
\[
\textbf{Q3: A set is said to be finite if:}
\]
\[
\text{(A) It contains a fixed number of elements} \quad
\text{(B) It is empty} \quad
\text{(C) It has an infinite number of elements} \quad
\text{(D) None of these}
\]
\[
\textbf{Answer: (A) It contains a fixed number of elements}
\]
\[
\textbf{Q4: The power set of a set A is:}
\]
\[
\text{(A) The set of all subsets of A} \quad
\text{(B) The set of all elements of A} \quad
\text{(C) The set of all proper subsets of A} \quad
\text{(D) None of these}
\]
\[
\textbf{Answer: (A) The set of all subsets of A}
\]
\[
\textbf{Q5: Two sets A and B are said to be disjoint if:}
\]
\[
\text{(A) A is a subset of B} \quad
\text{(B) A and B have no elements in common} \quad
\text{(C) A is equal to B} \quad
\text{(D) None of these}
\]
\[
\textbf{Answer: (B) A and B have no elements in common}
\]
\[
\textbf{Q6: The intersection of two sets A and B is:}
\]
\[
\text{(A) The set of elements present in A but not in B} \quad
\text{(B) The set of elements present in both A and B} \quad
\text{(C) The set of elements present in A or B or both} \quad
\text{(D) None of these}
\]
\[
\textbf{Answer: (B) The set of elements present in both A and B}
\]
\[
\textbf{Q7: In logic, the negation of a statement P is true when:}
\]
\[
\text{(A) P is true} \quad
\text{(B) P is false} \quad
\text{(C) P is both true and false} \quad
\text{(D) None of these}
\]
\[
\textbf{Answer: (B) P is false}
\]
\[
\textbf{Q8: The union of two sets A and B is:}
\]
\[
\text{(A) The set of elements present in A but not in B} \quad
\text{(B) The set of elements present in both A and B} \quad
\text{(C) The set of elements present in A or B or both} \quad
\text{(D) None of these}
\]
\[
\textbf{Answer: (C) The set of elements present in A or B or both}
\]
\[
\textbf{Q9: A statement in logic that cannot be proven or disproven is called:}
\]
\[
\text{(A) A contradiction} \quad
\text{(B) A tautology} \quad
\text{(C) An axiom} \quad
\text{(D) None of these}
\]
\[
\textbf{Answer: (C) An axiom}
\]
\[
\textbf{Q10: The Cartesian product of two sets A and B is:}
\]
\[
\text{(A) The set of all ordered pairs (a, b) where a is in A and b is in B} \quad
\text{(B) The set of elements common to both A and B} \quad
\text{(C) The set of elements unique to either A or B} \quad
\text{(D) None of these}
\]
\[
\textbf{Answer: (A) The set of all ordered pairs (a, b) where a is in A and b is in B}
\]