R S Aggarwal Solutions for Exercise 2: EXERCISE 2B

If $A$ and $B$ be two sets such that $n\left(A\right)=3, n\left(B\right)=4$ and $n(A\cap B)=2$ then find:

$n(A\times B)$

If $A$ and $B$ be two sets such that $n\left(A\right)=3, n\left(B\right)=4$ and $n(A\cap B)=2$ then find:

$n(B\times A)$

If $A$ and $B$ be two sets such that $n\left(A\right)=3, n\left(B\right)=4$ and $n(A\cap B)=2$ then find:

$n\left\{\right(A\times B)\cap (B\times A\}$

For any two sets $A$ and $B,$ show that $A\times B$ and $B\times A$ have an element in common if and only if $A$ and $B$ have an element in common.

Let $A=\{1,2\}$ and $B=\{2,3\}.$ Then, write down all possible subsets of $A\times B$

Let $A=\{a,b,c,d\}, B=\{c,d,e\}$ and $C=\{d,e,f,g\}.$ Then verify each of the following identities:

$A\times (B\cap C)=(A\times B)\cap (A\times C)$

Let $A=\{a,b,c,d\},B=\{c,d,e\}$ and $C=\{d,e,f,g\}.$ Then verify each of the following identities:

$A\times (B-C)=(A\times B)-(A\times C)$

Let $A=\{a,b,c,d\},B=\{c,d,e\}$ and $C=\{d,e,f,g\}.$ Then verify the identities:

$(A\times B)\cap (B\times A)=(A\cap B)\times (A\cap B)$