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.
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.