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) $C \cap D$

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Solution

$A = {x : x is a natural number} = {1, 2, 3, 4, 5.....}$
$B = {x : x is an even natural number} = {2, 4, 6, 8 . . . . .}$
$C = {x : x is an odd natural number} = {1, 3, 5, 7, 9 . . . . . . .}$
$D = {x : x is a prime number} = {2, 3, 5, 7 . . . .}$
(i) $A \cap B = {x : x is a even natural number} = B$
(ii) $A \cap C = {x : x is an odd natural number} = C$
(iii) $A \cap D = {x : x is a prime number} = D$
(iv) $B \cap C = ϕ$
(v) $B \cap D = {2}$
(vi) $C \cap D = {x : x is odd prime number}$

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If A = {x: x is a natural number}, B ={x: x is an even natural number}

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