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} and D = {x : x is a prime number }, find $A /cap B$

Answer 1

we know, if two sets A and B are given then, intersection of A and B is the set of all distinct elements that are in both A and B. it is denoted by $A\cap B$ or $B\cap A$. in figure, shaded region indicates $A\cap B$.
and A union B is the set of all distinct elements that are in Both A or B. it is denoted by $A\cup B$. in 2nd figure, it is clearly shown.

now come to the question,
given, A = {x : x is a natural number}
e.g., A = {1, 2, 3, 4, 5, 6, ...... }
B = {x : x is an even natural number }
e.g., B = {2, 4, 6, 8, 10, ....... }

now, $A\cap B$ = {1, 2, 3, 4, 5, 6, .... } $\cap$ {2, 4, 6, 8, 10, .....}
= {2, 4, 6, 8, 10, ... } = B

hence, $A\cap B=B$

Answer 2

Answer:

A cap B = { 2,4,6,8,...} = B

Step-by-step explanation:

A = { x:x is a natural number }

=> A = { 1,2,3,4,5,,6,.....}

B = { x :x is an even natural number }

=> B = { 2,4,6,8,10,... }

A cap B = { x:x€A and x€ B }

= { 1,2,3,4,...} Cap { 2,4,6,8,...}

= { 2,4,6,8,10,...}

= B

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