Chapter 31: Mathematical Reasoning  – Exercise 31.4

Mathematical Reasoning – Exercise – 31.4 – Q.1

(i)

The negation of the statement:

For every x ∈ N, x + 3 < 10

is

There exists x ∈ N such that x + 3 ≥ 10.

(ii)

The negation of the statement:

There exists x ∈ N, x + 3 = 10

is

For every x ∈ N, x + 3 ≠ 10

 

Mathematical Reasoning – Exercise – 31.4 – Q.2

(i)

The negation of the statement:

All the students completed their homework.

is

some of the students did not complete their home work.

(ii)

The negation of the statement:

There exists a number which is equal to its square.

is

For every real number x, x²≠ x.