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NCERT Solutions for class 14 Maths | Chapter 14 - Mathematical Reasoning

(1) Which of the following is a statement
[A] x is a real number
[B] Switch of the fan
[C] 6 is a natural number
[D] Let me go
Answer: 6 is a natural number
(2) Which of the following is not a statement
[A] The product of (-1) and 8 is 8
[B] All complex number are real number
[C] Today is windy day
[D] All of the above
Answer: All of the above

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(3) The converse of the statement p ⇒ q is
[A] p ⇒ q
[B] q ⇒ p
[C] ~p ⇒ q
[D] ~q ⇒ p
Answer: q ⇒ p
(4) Which of the following is the conditional p → q
[A] q is sufficient for p
[B] p is necessary for q
[C] p only if q
[D] if q then p
Answer: p only if q
(5) If (p and q) is false then
[A] p is true and q is false
[B] p is false and q is false
[C] p is false and q is true
[D] all of the above
Answer: all of the above
(6) Which of the following statement is a conjunction
[A] Ram and Shyam are friends
[B] Both Ram and Shyam are friends
[C] Both Ram and Shyam are enemies
[D] None of these
Answer: None of these
(7) Which of the following is a statement
[A] x is a real number
[B] Switch of the fan
[C] 6 is a natural number
[D] Let me go
Answer: 6 is a natural number
(8) If (p or q) is true, then
[A] p is true and q is false
[B] p is true and q is true
[C] p is false and q is true
[D] All of the above
Answer: All of the above
(9) Which of the following is a compound statement
[A] Sun is a star
[B] I am a very strong boy
[C] There is something wrong in the room
[D] 7 is both odd and prime number.
Answer: 7 is both odd and prime number.
(10) Which of the following is a statement
[A] I will go tomorrow
[B] She will come today
[C] 3 is a prime number
[D] Tomorrow is Friday
Answer: 3 is a prime number
(11) Which of the following is true
[A] A prime number is either even or odd
[B] √3 is irrational number.
[C] 24 is a multiple of 2, 4 and 8
[D] Everyone in India speaks Hindi.
Answer: Everyone in India speaks Hindi.
(12) Which of the following is not a negation of the statement A natural number is greater than zero
[A] A natural number is not greater than zero
[B] It is false that a natural number is greater than zero
[C] It is false that a natural number is not greater than zero
[D] None of these
Answer: It is false that a natural number is not greater than zero
(13) The contra-positive of the statement if p then q is
[A] if ~p then q
[B] if p then ~q
[C] if q then p
[D] if ~q then ~p
Answer: if ~q then ~p
(14) Which of the following is not a negation of the statement A natural number is greater than zero
[A] A natural number is not greater than zero
[B] It is false that a natural number is greater than zero
[C] It is false that a natural number is not greater than zero
[D] None of these
Answer: It is false that a natural number is not greater than zero
(15) The converse of the statement if a number is divisible by 10, then it is divisible by 5 is
[A] if a number is not divisible by 5, then it is not divisible by 10
[B] if a number is divisible by 5, then it is not divisible by 10
[C] if a number is not divisible by 5, then it is divisible by 10
[D] if a number is divisible by 5, then it is divisible by 10
Answer: if a number is divisible by 5, then it is divisible by 10
(16) The connective in the statement 2 + 7 > 9 or 2 + 7 < 9 is
[A] and
[B] or
[C] >
[D] <
Answer: or
(17) The contra-positive of the statement If a triangle is not equilateral, it is not isosceles is
[A] If a triangle is not equilateral, it is not isosceles
[B] If a triangle is equilateral, it is not isosceles
[C] If a triangle is not equilateral, it is isosceles
[D] If a triangle is equilateral, it is isosceles
Answer: If a triangle is equilateral, it is isosceles
(18) Which of the following is not a statement
[A] 8 is less than 6.
[B] Every set is finite set.
[C] The sun is a star.
[D] Mathematics is fun.
Answer: Mathematics is fun.
(19) The negation of the statement The product of 3 and 4 is 9 is
[A] It is false that the product of 3 and 4 is 9
[B] The product of 3 and 4 is 12
[C] The product of 3 and 4 is not 12
[D] It is false that the product of 3 and 4 is not 9
Answer: It is false that the product of 3 and 4 is 9
(20) Sentence involving variable time such as today, tomorrow, or yesterday are
[A] Statements
[B] Not statements
[C] may or may not be statements
[D] None of these
Answer: Not statements

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