Welcome to Class 11 Maths MCQ – Mathematical Reasoning chapter, Here, we’ve curated a set of 20 multiple-choice questions. Each MCQ is followed by the correct answer and an explanation. Go ahead and take this MCQ to test your knowledge of Mathematical Reasoning.
1. If the statement "If it rains, then the match will be canceled" is true, which is also true?
a) If it does not rain, the match will not be canceled.
b) If the match is not canceled, then it did not rain.
c) If the match is canceled, then it rained.
d) If it rains, the match will happen.
Answer:
b) If the match is not canceled, then it did not rain.
Explanation:
This is the contrapositive of the original statement.
2. Which of the following is the converse of "If it is a square, then it has four sides"?
a) If it has four sides, then it is a square.
b) If it is not a square, then it doesn't have four sides.
c) If it doesn't have four sides, then it isn't a square.
d) It is a square only if it has four sides.
Answer:
a) If it has four sides, then it is a square.
Explanation:
The converse swaps the hypothesis and the conclusion.
3. A statement and its negation are:
a) Always true
b) Always false
c) Sometimes true and sometimes false
d) One is true and the other is false
Answer:
d) One is true and the other is false
Explanation:
A statement and its negation can never both be true at the same time.
4. Which is the inverse of "If I study, then I will pass"?
a) If I do not study, then I will not pass.
b) If I study, then I will not pass.
c) If I pass, then I studied.
d) If I do not pass, then I did not study.
Answer:
a) If I do not study, then I will not pass.
Explanation:
The inverse negates both the hypothesis and the conclusion.
5. Which type of statement is "All roses are flowers"?
a) Conditional
b) Biconditional
c) Conjunction
d) Universal
Answer:
d) Universal
Explanation:
It makes a general claim about all members of a certain set.
6. "p and not q" is represented by:
a) p ∨ ~q
b) p ∧ ~q
c) ~p ∧ q
d) ~p ∨ q
Answer:
b) p ∧ ~q
Explanation:
The symbol '∧' represents 'and' and '~' represents 'not'.
7. Which is a contradiction?
a) x is odd and x is not odd.
b) x is even or x is not even.
c) If x is prime, then x is odd.
d) x is greater than 2 or less than 5.
Answer:
a) x is odd and x is not odd.
Explanation:
The statement contains conflicting assertions, making it a contradiction.
8. The negation of "Some cats are black" is:
a) No cats are black.
b) All cats are black.
c) Some cats are not black.
d) Every cat is black.
Answer:
a) No cats are black.
Explanation:
The negation of "some" is "no".
9. Which statement is a tautology?
a) p or not p
b) p and not p
c) p implies q
d) If p then q and if q then p
Answer:
a) p or not p
Explanation:
A tautology is always true, and the statement "p or not p" meets that criteria.
10. "If and only if" is represented by:
a) ∧
b) ∨
c) →
d) ↔
Answer:
d) ↔
Explanation:
"If and only if" is a biconditional, represented by '↔'.
11. The compound statement "p or q" is false when:
a) p is true; q is true.
b) p is false; q is true.
c) p is true; q is false.
d) p is false; q is false.
Answer:
d) p is false; q is false
Explanation:
An 'or' statement is only false when both components are false.
12. Which is the contrapositive of "If you run, you sweat"?
a) If you sweat, you run.
b) If you don't run, you don't sweat.
c) If you don't sweat, you didn't run.
d) If you run, you don't sweat.
Answer:
c) If you don't sweat, you didn't run.
Explanation:
The contrapositive negates and swaps the hypothesis and conclusion.
13. Which is a disjunction?
a) p and q
b) p but not q
c) p if q
d) p or q
Answer:
d) p or q
Explanation:
A disjunction is an 'or' statement.
14. If a statement "If p then q" is true, which must also be false?
a) If q then p.
b) If not p then not q.
c) If not q then not p.
d) p and not q.
Answer:
d) p and not q.
Explanation:
The statement implies that p being true forces q to be true.
15. "Neither p nor q" can be represented as:
a) ~p ∧ ~q
b) p ∨ q
c) ~p ∨ q
d) p ∧ ~q
Answer:
a) ~p ∧ ~q
Explanation:
The statement is true when both p and q are false.
16. The statement "All integers are real numbers" is:
a) Always true
b) Always false
c) Sometimes true
d) Neither true nor false
Answer:
a) Always true
Explanation:
All integers are a subset of real numbers.
17. "If not q then p" can be represented as:
a) q → p
b) p → q
c) ~q → p
d) p → ~q
Answer:
c) ~q → p
Explanation:
The 'not' applies to q and then implies p.
18. Which statement is equivalent to "p if and only if q"?
a) (p → q) ∧ (q → p)
b) (p → q) ∨ (q → p)
c) (p ∧ q) → (q ∧ p)
d) (p ∨ q) → (q ∨ p)
Answer:
a) (p → q) ∧ (q → p)
Explanation:
Biconditional is equivalent to both forward and backward implications.
19. If two statements are logically equivalent, then:
a) One is true and the other is false.
b) They have the same truth values.
c) They are contradictions.
d) One implies the other.
Answer:
b) They have the same truth values.
Explanation:
Logically equivalent statements have the same truth value for every possible input.
20. The statement "p and not p" is called:
a) Tautology
b) Contradiction
c) Contingency
d) Biconditional
Answer:
b) Contradiction
Explanation:
The statement can never be true, making it a contradiction.