CBSE Class 11 Mathematics HOTs Mathematical Reasoning

Question. For the statement “17 is a real number or a positive integer”, the “or” is
(a) Inclusive
(b) Exclusive
(c) Only (a)
(d) None of these
Answer : A

Question. ~ p ∧ q is logically equivalent to
(a) p → q
(b) q → p
(c) ~ (p → q)
(d) ~ ( q→ p)
Answer : D

Question. If p is false and q is true, then
(a) p ∧ q is true
(b) p ∨ ~ q is true
(c) q ∧ p is true
(d) p ⇒ q is true
Answer : D

Question. The false statement in the following is
(a) p ∧ (~ p) is contradiction
(b) (p ⇒ q) ⇔ (~ q ⇒ ~ p) is a contradiction
(c) ~ (~ p) ⇔ p is a tautology
(d) p ∨ (~ p) ⇔ p is a tautology
Answer : B

Question. The conditional (p ∧ q) ⇒ p is
(a) A tautology
(b) A fallacy i.e., contradiction
(c) Neither tautology nor fallacy
(d) None of these
Answer : A

Question. Let p and q be any two logical statements and r : p → (: p ∨ q) . If r has a truth value F, then the truth values of p and q are respectively :
(a) F, F
(b) T, T
(c) T, F
(d) F, T
Answer : C

Question. If p : Ashok works hard
q : Ashok gets good grade
The verbal form for (~ p →q) is
(a) If Ashok works hard then gets good grade
(b) If Ashok does not work hard then he gets good grade
(c) If Ashok does not work hard then he does not get good grade
(d) Ashok works hard if and only if he gets grade
Answer : B

Question. Which of the following is false?
(a) p ∨ ~ p is a tautology
(b) ~ (~p) ↔ p is a tautology
(c) p ∧ ~ p is a contradiction
(d) ((p ∧ q) → q) → p is a tautology
Answer : B

Question. If p ⇒ (~ p ∨ q) is false, then truth values of p and q are respectively
(a) F. T
(b) F, F
(c) T, T
(d) T, F
Answer : D

Question. Which of the following is a contradiction?
(a) (p ∧ q)∧ ~ (p ∨ q)
(b) p ∨ (~ p ∧ q)
(c) (p ⇒ q) ⇒ p
(d) None of these
Answer : A

Question. (p ∧ ~ q) ∧ (~ p ∧ q) is
(a) A tautology
(b) A contradiction
(c) Both a tautology and a contradiction
(d) Neither a tautology nor a contradiction
Answer : B

Question. In the truth table for the statement ( p → q) ↔ (~ p ∨ q), the last column has the truth value in the following order is
(a) TTFF
(b) FFFF
(c) TTTT
(d) FTFT
Answer : C

Question. ~ ((~ p) ∧ q) is equal to
(a) p ∨ (~ q)
(b) p ∨ q
(c) p ∧ (~ q)
(d) ~ p ∧ ~ q
Answer : A

Question. Negation of “2 + 3 = 5 and 8 < 10” is
(a) 2 + 3 ¹ 5 and < 10
(b) 2 + 3 = 5 and 8 </ 10
(c) 2 + 3 ¹ 5 or 8 </ 10
(d) None of these
Answer : C

Question. The negation of the compound proposition p ∨ (~ p ∨ q) is
(a) ( p ∧ ~ q) ∧ ~ p
(b) ( p ∧ ~ q) ∨ ~ p
(c) ( p ∨ ~ q) ∨ ~ p
(d) None of these
Answer : A

Question. If p and q are two statements, then (p ⇒ q) ⇔ (–q ⇒ ~ p) is a
(a) contradiction
(b) tautology
(c) neither (a) nor (b)
(d) None of these
Answer : B

Question. Which of the following is true?
(a) p ⇒ q ≡ ~ p ⇒ ~ q
(b) ~ (p ⇒ ~ q) ≡ ~ p∧q
(c) ~ (~ p ⇒ ~ q) ≡ ~ p∧q
(d) ~ (~ p ⇔ q) ≡ [~ (p ⇒ q)∧ ~ (q ⇒ p)]
Answer : C

Question. The negation of (p ∨ q)∧ (p ∨ ~ r) is
(a) (~ p ∧ ~ q) ∨ (q ∧ ~ r)
(b) (~ p ∧ ~ q) ∨ (~ q ∧ r)
(c) (~ p ∧ ~ q) ∨ (~ q ∧ r)
(d) (p ∧ q) ∨ (~ q ∧ ~ r)
Answer : C

Question. Identify the false statements
(a) ~ [p ∨ (~ q)] ≡ (~ p) ∨ q
(b) [p ∨ q] ∨ (~ p) is a tautology
(c) [p ∧ q) ∧ (~ p) is a contradiction
(d) ~ [p ∨ q] ≡ (~ p) ∨ (~ q)
Answer : D

Question. If the compound statement p → (~ p ∨ q) is false then the truth value of p and q are respectively
(a) T, T
(b) T, F
(c) F, T
(d) F, F
Answer : B

Question. The contrapositive of p → (~q → ~r) is
(a) (~ q ∧ r) → ~ p
(b) (q → r) → ~p
(c) (q ∨ ~r) → ~ p
(d) None of these
Answer : A

Question. Negation of the statement (p ∧ r) → (r ∨ q) is
(a) ~ (p ∧ r) → ~ (r ∨ q)
(b) (~p ∨ ~r) ∨ (r ∨ q)
(c) (p ∧ r) ∧ (r ∧ q)
(d) (p ∧ r) ∧ (~ r ∧ ~q)
Answer : D

Question. The inverse of the statement (p ∧ ~ q) → r is
(a) ~ (p ∨ ~q) → ~ r
(b) (~p ∧ q) → ~ r
(c) (~p ∨ q) → ~ r
(d) None of these
Answer : C

Question. Let p, q and r be any three logical statements.
Which of the following is true?
(a) ~ [p ∧ (~ q)] ≡ (~ p) ∧ q
(b) ~ [(p ∨ q) ∧ (~ r) ≡ (~ p) ∨ (~ q) ∨ (~ r)
(c) ~ [p ∨ (~ q)] ≡ (~ p) ∧ q
(d) ~ [p ∨ (~ q)] ≡ (~ p) ∧ ~ q
Answer : C

Question. Let A, B, C and D be four non-empty sets. The contrapositive statement of “If A ⊆ B and B ⊆ D, then A ⊆ C ” is:
(a) If A ⊄ C, then A ⊆ B and B ⊆ D
(b) If A ⊆ C, then B ⊂ A or D ⊂ B
(c) If A ⊄ C, then A ⊄ B and B ⊆ D
(d) If A ⊄ C, then A ⊄ B or B ⊄ D
Answer : D