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 $C \cap D$

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 = {1, 2, 3, 5, 7, 11, 13, .....}

so, $C\cap D$ = {1, 3, 5, 7, 9, 11, 13, ...} $\cap$ {1, 2, 3, 5, 7, 11, 13....}
= {1, 3, 5, 7, 11, 13, 17 .... } = {x : x is an odd prime number}

hence, $C\cap D=\{x:x\textbf{is an odd prime number}\}$

Answer 2

Solution :

C = { x:x is an odd natural number }

=> C = { 1,3,5,7,...}

D = { x : x is a prime number }

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

C cap D = {1,3,5,7,9,11,...}cap{ 2,3,5,7,11...}

= { 3,5,11,13,17, ....}

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