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 :

(i) $A\cap B$ (ii) $A\cap C$ (iii) $A\cap D$

(iv) $B\cap C$ (v) $B\cap D$ (vi) $C\cap D$

Answer 1

Here A = {x : x is a natural number}

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

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

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

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

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

and D = {x : x is a prime number}

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

(i) $A\cap B$ = {x : x is a natural number} $\cap$ {x : x is an even natural number}

= {x : x is an even natural number}

= B

(ii) $A\cap C$ = {x : x is a natural number} $\cap$ {x : x is an odd natural number}

= {x : x is an odd natural number}

= C

(iii) $A\cap D$ = {x : x is a natural number} $\cap$ {x : x is a prime number}

= {x : x is a prime number}

= D

(iv) $B\cap C$ = {x : x is an even natural number} $\cap$ {x : x is an odd natural number}

= $\Phi$

(v) $B\cap D$ = {x : x is an even natural number} $\cap$ {x : x is a prime number}

= {2}

(vi) $C\cap D$ = {x : x is an odd natural number} $\cap$ {x : x is a prime number}

= {x : x is an odd prime number} = D -{2}