Question

C={ x/x € N , x <7 and x > 11 } is this an empty set?​

Answer 1

Correct Question :-

C = {x | x ∈ N, x < 7 and x > 11}

Is this an Empty Set ?

SoluTion :-

Yes, it is an empty set.

Here, properties of x are,

x is an element of natural numbers

x is smaller than 7

x is greater than 11

⇒ The 2nd and 3rd properties do not satisfy x to be a natural number. As there is no natural number smaller than 7 and greater than 11.

Verification :-

Since, x < 7

Thus x could be - 1, 2, 3, 4, 5, 6 [Natural numbers]

But since, x > 11

1, 2, 3, 4, 5, 6 are not greater than 11

Thus, there is no such number.

So, there is no element of Set C.

⇒ Set C is void.