Class 11 Mathematics Mathematical Reasoning MCQs

Answer :  D


Question : Let p: Kiran passed the examination, q: Kiran is sad    
The symbolic form of a statement "It is not true that Kiran passed therfore he is said' is
(a) (~ p → q)
(b) (p → q)
(c) ~ (p → ~ q)
(d) ~ ( p ↔ q)

Answer :  B
 

Question : Consider the following statements    
P : Suman is brilliant
Q : Suman is rich
R : Suman is honest
The negation of the statement “Suman is brilliant and dishonest if and only if Suman is rich” can be expressed as
(a) ~ (Q ↔ (PΛ ~ R))   
(b) ~ Q ↔~ P Λ R
(c) ~ (PΛ ~ R) ↔Q
(d) ~ P Λ (Q ↔ ~ R)

Answer :  A


Question : The only statement among the following that is a tautology is    
(a) A Λ (A ∨ B)
(b) A ∨ (A Λ B)
(c) [A Λ (A → B)] → B
(d) B → [A Λ (A → B)]

Answer :  C


Question : If (p ∧ ~ r)⇒(q ∨r) is false and q and r are both false, then p is    
(a) True
(b) False
(c) May be true or false
(d) Data sufficient

Answer :  A


Question : If p, q, r are statement with truth vales F, T, F respectively then the truth value of p→(q → r) is    
(a) false
(b) true
(c) true if p is true
(d) none

Answer :  B


Question : In the truth table for the statement ~ ( ~ p ∨ ~ q),the last column has the truth value in the following order    
(a) TFFF
(b) TTFT
(c) FTTF
(d) FFFT

Answer :  A


Question : In the truth table for the statement ( ~ p → ~ q) ∧( ~ q → ~ p), the last column has the truth value in the following order is    
(a) TTTF
(b) FTTF
(c) TFFT
(d) TTTT
(d) (p Λ q) ∨ (~ q Λ ~ r).

Answer :  C


Question : Which of the following is the inverse of the proposition : “If a number is a prime then it is odd.”    
(a) If a number is not a prime then it is odd
(b) If a number is not a prime then it is odd
(c) If a number is not odd then it is not a prime
(d) If a number is not odd then it is a prime

Answer :  B


Question : If p ⇒ (q ∨ r) is false, then the truth values of p, q, r are respectively    
(a) T, F, F
(b) F, F, F
(c) F, T, T
(d) T, T, F

Answer :  A


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 :  B


Question : If p and q are true statement and r, s are false statements then the truth value of ~[(p∧~r)∨(~q ∨ s)] is    
(a) true
(b) false
(c) false if p is true
(d) none

Answer :  D


Question : In the truth table for the statement ( p ∧ q) →(q ∨ ~ p), the last column has the truth value in the following order is    
(a) TTFF
(b) FTTT
(c) TFTT
(d) TTTT

Answer :  D


Question : ~(p → q)→ [(~p) ∨ (~ q)] is    
(a) a tautology
(b) a contradiction
(c) neither a tautology nor contradiction     
(d) cannot come any conclusion

Answer :  A

Question : Which of the following is a contradiction?    
(a) (p Λ q)Λ ~ (p ∨ q)
(b) p∨ (-p Λ q)
(c) (p ⇒ q) ⇒ p        
(d) None of these

Answer :  A


Question : (p Λ ~ q) Λ (~ p ∨q) is    
(a) A contradiction
(b) A tautology
(c) Either (a) or (b)
(d) Neither (a) nor (b)

Answer :  A


Question : Which of the following is always true?       
(a) (p⇒q) ≡ ~ q⇒~ p
(b) ~ (p ∨ q) ≡ ∨ p ∨ ~ q
(c) ~ (p⇒q) ≡ p Λ ~ q
(d) ~ (p ∨ q) ≡ ~ p Λ ~ q

Answer :  C


Question : The propositions (p⇒~ p) Λ (~ p⇒p) is    
(a) Tautology and contradiction
(b) Neither tautology nor contradiction
(c) Contradiction
(d) Tautology

Answer :  C


Question : The negation of the statement (p Λ q) → (~ p ∨ r) is    
(a) (p Λ q) ∨ (p ∨ ~ r)
(b) (p Λ q) ∨ (p Λ ~ r)
(c) (p Λ q) Λ (p Λ~ r)
(d) p ∨ q

Answer :  C


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

Answer :  B

Question : If p, q, r are statement with truth values F, T, F respectively then the truth value of (~ p → ~ q) ∨ r is    
(a) true
(b) false
(c) false if r is true
(d) false if q is false

Answer :  B


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

Answer :  B


Question : The negation of the statement (p∨ q) Λ r is    
(a) (~ p ∨ ~ q) ∨ ~ q
(b) (~ p Λ ~ q) ∨ ~ r
(c) ~ (p ∨ q)→ r
(d) pΛq.

Answer :  B


Question : ~ (p ∨ q)∨ (~ p Λ q) is logically equivalent to    
(a) ~p
(b) p
(c) q
(d) ~q

Answer :  A


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

Answer :  C


Question : Let S be a non-empty subset of R. Consider the following statement : P : There is a rational number x Î S such that x > 0.    
Which of the following statements is the negation of the statement P ?
(a) There is no rational number x Î S such than x < 0.
(b) Every rational number x Î S satisfies x < 0.
(c) x Î S and x < 0 ⇒ x is not rational.
(d) There is a rational number x Î S such that x < 0.

Answer :  B


Question : Which of the following is not a statement in logic?    
(a) The sum of angles of a quadrilateral is 180°.
(b) Every statement has one truth value.
(c) 3 is an irrational number.
(d) x + 5 = 7, x Î Q.

Answer :  D


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

Answer :  D

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

Answer :  C


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

Answer :  D
 

Question : Negation of the proposition : If we control population growth, we prosper    
(a) If we do not control population growth, we prosper
(b) If we control population growth, we do not prosper
(c) We control population but we do not prosper
(d) We do not control population, but we prosper

Answer :  C


Question : The negation of (p ∨ q)Λ (p ∨ ~ r) is    
(a) (~ p Λ ~ q) ∨ (q Λ ~ r)
(b) (~ p Λ ~ q) ∨ (~ q Λ r)
(c) (~ p Λ ~ q) ∨ (~ q Λ r)

Answer :  C