# Mathematics Questions and Answers – Mathematical Reasoning – Validating Statements

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This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Mathematical Reasoning – Validating Statements”.

1. Which of the following statement is true?
a) 25 is divisible by 2 and 3
b) 12 is a positive and prime number
c) 13 is a positive and odd number
d) 49 is a square and a cube

Explanation: For a statement with ‘and’, if both statements are true then the given statement will be true.
In statement “25 is divisible by 2 and 3”, 25 is divisible by 2 is true but 25 is divisible by 3 is false so it is false statement.
In statement “12 is a positive and prime number”, 12 is a positive number is true but 12 is a prime number is false so it is a false statement.
In statement “13 is a positive and odd number”, both statements i.e. 13 is a positive number and 13 is an odd number are true so it is a true statement.
In statement “49 is a square and a cube”, 49 is a square is true but 49 is a cube is false so it is a false statement.

2. Which of the following statements is false?
a) Delhi and Mumbai are cities of India
b) Chandigarh is capital of Punjab and Haryana
c) 81 is a square and cube
d) 16 is even number and divisible by 8

Explanation: Since Delhi and Mumbai both are cities in India so “Delhi and Mumbai are cities of India” is true.
Since Chandigarh is the capital of both states Punjab and Haryana so “Chandigarh is capital of Punjab and Haryana” is true.
Since 81 is a square and not a cube so “81 is a square and cube” is false.
Since 16 is even number and is also divisible by 8 so “16 is even number and divisible by 8” is true.

3. Which of the following statement is false?
a) 24 is even number or odd number
b) 15 is prime or divisible by 3
c) 71 is odd number or prime
d) Japan or China is in India

Explanation: 24 is even number so “24 is even number or odd number” is correct. 15 is divisible by 3 so “15 is prime or divisible by 3” is true. 71 is prime as well as odd so “71 is odd number or prime” is true. Neither Japan nor China is in India so “Japan or China is in India” is false.

4. In direct method to prove statement “If p then q” is valid or not, we assume p to be __________ and prove q to be _____________
a) true, false
b) true, true
c) false, false
d) false, true

Explanation: In direct method, we assume p to be true and use it to prove that q is also true.
There is no case for p to be false in direct method.

5. In contrapositive method to prove statement “If p then q” is valid or not, we assume p to be __________ and prove q to be ______________
a) true, false
b) true, true
c) false, false
d) false, true

Explanation: In contrapositive method, we assume p to be false and use it to prove that q is also false.
There is no case for p to be true in direct method.

6. “If p then q” is true when _______________
a) p => q
b) q => p
c) p => not q
d) both p => q and q => p

Explanation: If p then q statement will be true if-
If p is true then q must be true and if q is true then p must be true.

Sanfoundry Global Education & Learning Series – Mathematics – Class 11. 