Question

1. Which of the following sets are empty?
Justiſy,
a. (x:x N and 3 <x<4)
b. (x:x is a prime number lying between
17 and 19)
c. (x:x is prime and 19 SXS 23)
d. (x:x° + 2 = 0 and x e N)
e. (x:x e W and 13 sxs 14)
f. (Vowels in the word WISE)
​

Answer 1

Answer:

Parts (a) , (b) , (c) , (d) and (e) are empty

Step-by-step explanation:

Since

In Part (a)

x is natural number between 3 and 4 and we know no natural number exist between 3 and 4

So

Part (a) is empty.

Now

In Part (b)

x is prime number between 3 and 4 and we know no prime number exist between 17 and 19

So

Part (b) is empty.

Now

In Part (c)

x is prime number between 19 and 23 and we know no prime number exist between 19 and 23

So

Part (c) is empty.

Now

In Part (d)

x is natural number which satisfy the equation

     x^0 + 2 = 0

⇒      1 + 2 = 0                            ∵ x^0 = 1   ,    ∀ x ∈ N

but     1 + 2 ≠ 0

So

No any natural number exist which satisfy the condition

Thus

Part (d) is empty.

Now

In Part (e)

x is whole number between 13 and 14 and we know no whole number exist between 13 and 14

So

Part (e) is empty.

Now

In Part (f)

we have to find the vowels in word WISE which are I and E

So

Part (f) is not empty.