# Let A=

Question:

Let $A=\{x: x \in N\}, B=\{x: x-2 n, n \in N\}, C=\{x: x=2 n-1, n \in N\}$ and $D=\{x: x$ is a prime natural number\}. Find:

(i) $A \cap B$

(ii) $A \cap C$

(iii) $A \cap D$

(iv) $B \cap C$

(v) $B \cap D$

(vi) $C \cap D$

Solution:

$A=\{x: x \in N\}=\{1,2,3, \ldots\}$

$B=\{x: x-2 n, n \in N\}=\{2,4,6,8, \ldots\}$

$C=\{x: x=2 n-1, n \in N\}=\{1,3,5,7, \ldots\}$

D = {x:x is a prime natural number.} = {2, 3, 5, 7,...}

(i) $A \cap B=B$

(ii) $A \cap C=C$

(iii) $A \cap D=D$

(iv) $B \cap C=\phi$

(v) $B \cap D=\{2\}$

(vi) $C \cap D=D-\{2\}$