Arts (English Medium) Class 11 - CBSE Question Bank Solutions for Mathematics

Write down the negation of following compound statements

x = 2 and x = 3 are roots of the Quadratic equation x² – 5x + 6 = 0.

Write down the negation of following compound statements

A triangle has either 3-sides or 4-sides.

Write down the negation of following compound statements

35 is a prime number or a composite number

Write down the negation of following compound statements

All prime integers are either even or odd.

Write down the negation of following compound statements

|x| is equal to either x or – x.

Write down the negation of following compound statements

6 is divisible by 2 and 3.

Rewrite the following statements in the form of conditional statements

The square of an odd number is odd.

Rewrite the following statements in the form of conditional statements

You will get a sweet dish after the dinner.

Rewrite the following statements in the form of conditional statements

You will fail, if you will not study.

Rewrite the following statements in the form of conditional statements

The unit digit of an integer is 0 or 5 if it is divisible by 5.

Rewrite the following statements in the form of conditional statements

The square of a prime number is not prime.

Rewrite the following statements in the form of conditional statements

2b = a + c, if a, b and c are in A.P.

Form the biconditional statement p ↔ q, where
p: The unit digit of an integer is zero.
q: It is divisible by 5.

Form the biconditional statement p ↔ q, where
p: A natural number n is odd.
q: Natural number n is not divisible by 2.

Form the biconditional statement p ↔ q, where
p: A triangle is an equilateral triangle.
q: All three sides of a triangle are equal.

Identify the Quantifiers in the following statements.

There exists a triangle which is not equilateral.

Identify the Quantifiers in the following statements.

For all real numbers x and y, xy = yx.

Identify the Quantifiers in the following statements.

There exists a real number which is not a rational number.

Identify the Quantifiers in the following statements.

For every natural number x, x + 1 is also a natural number.

Identify the Quantifiers in the following statements.

For all real numbers x with x > 3, x 2 is greater than 9.