Class 11 Mathematics Mathematical Reasoning MCQs Set 02

Question: Which of the following statement is a contradiction?
a) (~ p ∨ ~ q) ∨ (p ∨ ~ q)
b) (p → q) ∨ (p ∧ ~ q)
c) (~ p ∧ q) ∧ (~ q)
d) (~ p ∧ q) ∨ (~ q)
Answer: c

Question: Let R be the set of real numbers and x∈ R . Then, x +3= 8 is
a) open statement
b) a true statement
c) false statement
d) None of the options
Answer: a

Question: The negation of the 'statement, if a quadrilateral is a square, then it is a rhombus' is
a) if a quadrilateral is not a square, then it is a rhombus
b) if a quadrilateral is a square, then it is not a rhombus
c) a quadrilateral is a square and it is not a rhombus
d) a quadrilateral is not a square and it is a rhombus
Answer: c

Question: Which of the following is a statement?
a) x is a real number
b) Switch off the fan
c) 6 is a natural number
d) Let me go
Answer: c

Question: The negation of the 'statement, if a quadrilateral is a square, then it is a rhombus' is
a) if a quadrilateral is not a square, then it is a rhombus
b) if a quadrilateral is a square, then it is not a rhombus
c) a quadrilateral is a square and it is not a rhombus
d) a quadrilateral is not a square and it is a rhombus
Answer: c

Question: The contrapositive of the statement 'If 7 is greater than 5, then 8 is greater than 6' is
a) If 8 is greater than 6, then 7 is greater than 5
b) If 8 is not greater than 6, then 7 is greater than 5
c) If 8 is not greater than 6, then 7 is not greater than 5
d) If 8 is greater than 6,then 7 is not greater than 5
Answer: c

Question: The conditional statement of 'You will get a sweet dish after the dinner' is
a) If you take the dinner, then you will get a sweet dish
b) If you take the dinner, you will get a sweet dish
c) You get a sweet dish if and only if you take the dinner
d) None of the options
Answer: a

Question: If (q ∧ – r) ⇒(q ∨ r) is false, then p is
a) True
b) False
c) May be true and false
d) None of the options
Answer: a

Question: Which of the following is not a proposition ?
a) √3 is a prime
b) √2 is irrational
c) Mathematics is interesting
d) 5 is an even integer
Answer: c

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

Question: If ~ ( p ∧ q) is false, then corresponding values of pand q are, respectively
a) T, T
b) T, F
c) F, T
d) None of the options
Answer: a

Question: The negation of the statement '72 is divisible by 2 and 3' is
a) 72 is not divisible by 2 or 72 is not divisible by 3
b) 72 is not divisible by 2 and 72 is not divisible by 3
c) 72 is divisible by 2 and 72 is not divisible by 3
d) 72 is not divisible by 2 and 72 is divisible by 3
Answer: a

Question: Which of the following sentences is/are not statements?
a) There are 35 days in a month.
b) Mathematics is difficult.
c) The square of a number is an even number.
d) The side of a quadrilateral have equal lengths.
Answer(b ,c,d)

Question: The statement ~ (~ p ∨ ~ q) is
a) tautology
b) contradiction
c) contigency
d) None of the options
Answer: c

Question: Which of the following is not a statement?
a) Smoking is injurious to health
b) 2 + = 2 4
c) 2 is the only even prime number
d) Come here
Answer: d

Question: The negation of the statement 'If become a teacher, then I will open a school', is
a) I will become a teacher and I will not open a school
b) Either I will not become a teacher or I will not open a school
c) Neither I will become a teacher nor I will open a school
d) I will not become a teacher or I will open a school
Answer: c

Question: If p, q and r are simple propositions, then ( p ∧ q) ∧ (q ∧ r) is true, then
a) p, q and r are true
b) p, q are true and r is false
c) p is true and q, r are false
d) p, q and r are false
Answer: a

Question: Statement ( 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: Which of the following is not logically equivalent to the following proposition? 'A real number is either rational or irrational'
a) If a number is neither rational nor irrational, then it is not real
b) If a number is not a rational or not an irrational, then it is not real
c) If a number is not real, then it is neither rational or irrational
d) If a number is real, then it is rational or irrational
Answer: b

Question: If p, q and r are simple proposition, then(~ p ∨ q)⇒r is true, when p, q and r are, respectively
a) T, F, T
b) T, T, T
c) T, F, F
d) F, F, F
Answer(a,b)

Question: Which of the following is wrong?
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: d

Question: Which of the following is wrong statement?
a) p → q is logically equivalent to ~ p ∨ q
b) If the truth values of p, q, r are T, F, T respectively, then the truth value of (p ∨ q) ∧ (q ∨ r ) is T
c) ~ (∨ q ∨ q ∨ r ) ≡ ~ p ∧ ~ q ∧ ~ r
d) The truth value of p ∧ ~ (p ∨ q) is always T
Answer: d