If A = {x : x ϵ N}, B = {x : x ϵ N and x is even), C = {x : x ϵ N and x is odd} and D = {x : x ϵ N and x is prime} then find:
If $A=\{x: x \in N\}, B=\{x: x \in N$ and $x$ is even), $C=\{x: x \in N$ and $x$ is odd $\}$ and $D=\{x: x \in N$ and $x$ is prime $\}$ then find:
(i) $A \cap B$
(ii) $A \cap C$
(iii) $A \cap D$
(iv) $B \cap C$
(v) B $\cap$ D
(vi) $C \cap D$
Given; A = {x : x ϵ N}, B = {x : x ϵ N and x is even), C = {x : x ϵ N and x is odd} and D = {x : x ϵ N and x is prime}
(i) $A \cap B=\{x: x \in N$ and $x$ is even $\}$
(ii) $A \cap C=\{x: x \in N$ and $x$ is odd $\}$
(iii) $A \cap D=\{x: x \in N$ and $x$ is prime $\}$
(iv) $B \cap C=\Phi$ or \{\}
(v) $B \cap D=\{2\}[\because 2$ is the only even prime number]
(vi) $C \cap D=\{x: x \in N$ and $x$ is prime and $x \neq 2\}$
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