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 $A \cap D$

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, ....... }
C = {x : x is an odd natural number }
e.g., C = {1, 3, 5, 7, 9, ...... }
D = {x : x is a prime natural number }
e.g., D = {2, 3, 5, 7, 11, 13, .....}

so, $A\cap D$ = {1, 2, 3, 4, 5, 6....} $\cap$ {2, 3, 5, 7, 11, 13....}
= {2, 3, 5, 7, 11, 13.....} = D

hence, $A\cap D= D$

Answer 2

Answer:

A intersection D = { 2,3,5,7,...} = D

Step-by-step explanation:

A = { x:x is a natural number }

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

D = { x: x is a prime number }

=> D = { 2,3,5,7,11,... }

A intersection D

= Common elements in set A and D

= { 2,3,5,7,....}

= D

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