Mathematical Reasoning — Class 11 MCQs with Answers

Mathematical Reasoning — important questions & MCQs with answers (Class 11 Mathematics)

13 solved questions from this chapter's difficulty levels, each with its answer and explanation. The other 54 are timed and scored when you sign in.

1. Q1Easy

   A mathematical statement is:

   A.A sentence that is either true or false (not both)✓ Correct

   B.A question

   C.A command

   D.A wish

   Answer: A. A sentence that is either true or false (not both)

   Explanation: A statement is a declarative sentence with a definite truth value — true or false, never both — unlike questions, commands or wishes, which have no truth value to test at all.

2. Q2Easy

   Negation of "x is even":

   A.x is odd plus 1

   B.x is not even✓ Correct

   C.x is positive

   D.x = 0

   Answer: B. x is not even

   Explanation: Negation ~p simply denies p — "x is even" becomes "x is not even." Don't over-specify with "x is odd," which silently assumes x is an integer that the statement never stated.

3. Q3Easy

   Negation of statement p is denoted by:

   A.Both a and ¬p

   B.p'

   C.¬p only

   D.~p (or ¬p)✓ Correct

   Answer: D. ~p (or ¬p)

   Explanation: Negation is written with a tilde or the ¬ symbol: ~p or ¬p, both standard and interchangeable. A trailing prime, p′, denotes other operations in this chapter's notation, not negation.

4. Q4Easy

   Conjunction of p and q is denoted by:

   A.p ∨ q

   B.p ∧ q✓ Correct

   C.p → q

   D.p ↔ q

   Answer: B. p ∧ q

   Explanation: Conjunction ("and") uses the ∧ symbol: p ∧ q. Don't confuse it with ∨ (disjunction, "or") — the ∧ shape mirrors set intersection, both meaning "both conditions must hold."

5. Q5Easy

   'If p then q' is denoted by:

   A.p ∨ q

   B.p ↔ q

   C.p ∧ q

   D.p → q✓ Correct

   Answer: D. p → q

   Explanation: "If p then q" is the conditional, written p → q, with p as antecedent and q as consequent. Don't reach for ↔, which needs truth in both directions, not just one.

6. Q6Medium

   p AND q is true only when:

   A.Both false

   B.At least one is true

   C.Both p and q are true✓ Correct

   D.Always

   Answer: C. Both p and q are true

   Explanation: p ∧ q (AND) is true only when both p and q are true — read it straight off the conjunction's truth table; if either input is false, the whole conjunction turns false.

7. Q7Medium

   Negation of 'All triangles have 3 sides':

   A.All triangles have 4 sides

   B.No triangle has 3 sides

   C.Some triangle does not have 3 sides (or there exists a triangle...)✓ Correct

   D.Some triangles have 3 sides

   Answer: C. Some triangle does not have 3 sides (or there exists a triangle...)

   Explanation: Negating "All triangles have 3 sides" (∀x, P(x)) gives ∃x, ¬P(x): "Some triangle does not have 3 sides." Keeping the universal quantifier, as in "No triangle has 3 sides," is the wrong flip.

8. Q8Medium

   Compound statement: 'It is sunny, but cold'. Connective is:

   A.If-then

   B.Or

   C.And (conjunction)✓ Correct

   D.Not

   Answer: C. And (conjunction)

   Explanation: "But" logically behaves exactly like "and" — it still requires both parts to hold, just with an implied contrast in tone. Symbolically it's still conjunction, p ∧ q.

9. Q9Medium

   Converse of 'If p then q' is:

   A.If p then not q

   B.If not p then not q

   C.If not q then not p

   D.If q then p✓ Correct

   Answer: D. If q then p

   Explanation: The converse swaps hypothesis and conclusion: "if p then q" becomes "if q then p." It is NOT logically equivalent to the original — that equivalence belongs only to the contrapositive.

10. Q10Medium

    p ↔ q is true when:

    A.p and q have same truth values✓ Correct

    B.Different truth values

    C.Always

    D.Never

    Answer: A. p and q have same truth values

    Explanation: p ↔ q holds exactly when p and q agree — both true or both false. Different truth values always make the biconditional false, unlike →, which tolerates p false with q true.

11. Q11Hard

    Statement: 'If x > 0, then x² > 0' (where x is real). This is:

    A.Cannot determine

    B.False

    C.A true statement✓ Correct

    D.Conditional only

    Answer: C. A true statement

    Explanation: For any real x > 0, multiplying a positive number by itself always gives a positive result, so x² > 0 holds for every such x — the conditional is true with no counterexample possible.

12. Q12Hard

    Contrapositive of "if p then q" is:

    A.If ¬q then ¬p✓ Correct

    B.If ¬p then ¬q

    C.If q then p

    D.p iff q

    Answer: A. If ¬q then ¬p

    Explanation: The contrapositive negates both parts AND swaps their order: "if p then q" becomes "if not q then not p." It's the only transform sharing the original's truth table — converse and inverse aren't.

13. Q13Hard

    Negation of 'For every real number x, x² + 1 > 0':

    A.There exists a real number x such that x² + 1 ≤ 0✓ Correct

    B.For every real x, x² + 1 ≤ 0

    C.x² + 1 > 0

    D.For some real x, x² + 1 < 0

    Answer: A. There exists a real number x such that x² + 1 ≤ 0

    Explanation: Negating ∀x, x²+1>0 gives ∃x, x²+1≤0 — flip both the quantifier (∀ to ∃) and the inequality (> to ≤). Negating only to "<" leaves out the equality case and is incomplete.

Mathematical Reasoning — FAQs

More Class 11 Mathematics chapters

• 01Sets
• 02Relations and Functions
• 03Trigonometric Functions
• 04Principle of Mathematical Induction
• 05Complex Numbers and Quadratic Equations
• 06Linear Inequalities

Class 11 — other subjects

• Class 11 Biology chapters
• Class 11 Chemistry chapters
• Class 11 Computer Science chapters
• Class 11 English chapters
• Class 11 Physics chapters