 # Chapter 14 - Mathematical Reasoning

We suggest you go through these important questions of Chapter- 14 – Mathematical Reasoning, Class 11. Solving these questions on mathematical reasoning will help you score better marks in class 11. Here you can practice questions of chapter 14 which is a very important topic.

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Solve the following important questions on Mathematical Reasoning(CBSE Class 11) which would help you everywhere. Solving these kinds of questions is the best way to learn the topic thoroughly.

## Important Questions Class 11 Chapter 14 – Mathematical Reasoning

Question 1) Write the negation of the following statements

1) The number 3 is less than 1.

Solution: number 3 is more than 1.

2) Every whole number is less than 0.

Solution: Every whole number is more than 0.

3) The sun is cold

Solution: The sun is hot.

Question 2) Write a component statement for the following compound statements:

50 is a multiple of both 2 and 5.

Solution: p: 50 is multiple of 2

q: 50 is multiple of 5.

Question 3) Identify the quantifier in the following statement.

There exists a real number which is twice itself.

Solution: There exists.

Question 4) Write the following statement in the “if-then” form.

The banana trees will bloom if it stays warm for a month

Solution: “If it stays warm for a month then the Banana trees will bloom.”

Question 5) Show that the statement, p: if a is a real number such that a3 + 4a =0, then a is 0″, is true by direct method?

Solution: Let q and r are the statements given by q: a is a real number such that a3 + 4a =0

r: a is 0.

let q be true then

a is a real number such that a3 + 4a =0

a is a real number such that a(a2 + 4) =0

a = 0

r is true

So, q is true and r is true, so p is true.

Question 6) Verify by the method of contradiction that √7 is irrational.

Question 7) Check whether the following statement is true or not: “if a and b are odd integers, then ab is an odd integer”

Question 8) Check the validity of the following statements:

“square of the integer is positive or negative.”

Question 9) Write the contrapositive for the following statements: if a is a prime number, then a is odd.

Question 10) Write the negation of the given statement: All students live in dormitories.