Question

If A = {
x
:
x
is a natural number }, B = {
x
:
x
is an even natural number}
C = {
x
:
x
is an odd natural number}andD = {
x
:
x
is a prime number }, find
(i) A
∩
B (ii) A
∩
C (iii) A
∩
D
(iv) B
∩
C (v) B
∩
D (vi) C
∩
D

Answer 1

A would hence mean all natural numbers.

B would hence mean all even natural numbers. You can hence conclude that B is a part of A => B is a subset of A.

C would hence mean all odd natural numbers which again concludes that C is a subset of A.

D means all prime numbers. i.e. 2,3,5,7, again a part of set A Hence even D is a subset of A.

This is the general stuff. Coming to the question -

i) A
∩
B means all common elements between A and B.

which is nothing but the set B. (since all the common elements would be only odd natural numbers)

ii) A
∩
C In a similar fashion would mean only the Set C of all even natural numbers.

iii) A
∩
D would be the set D of all prime numbers. (Prime numbers are common in both A , D).

iv) now for B
∩
C.

If you have observed clearly then actually there is nothing common in sets B,C. Hence the solution will be a null set showed by { }.


Can u try out the others now?

Answer 2

Ya

Answer 3

Thank you sir .