Question

If A = {1, 2, 4} and B = {1, 2, 3}, represent following sets graphically :

(i) $A\times B$ (ii) $B\times A$

(iii) $A\times A$ (iv) $B\times B$

Answer 1

(i) We have,

A = {1, 2, 4} and B = {1, 2, 3}

$\therefore A\times B=\{1,2,4\}\times \{1,2,3\}$

$=\left\{\right(1,1),(1,2),(1,3),(2,1),(2,2),(2,3),(4,1),(4,2),(4,3\left)\right\}$

Hence, we represent A on the horizontal line and B on vertical line.

Graphical representation of $A\times B$ is as shown below :

(ii) We have,

A = {1, 2, 4} and B = {1, 2, 3}

$\therefore b\times A=\{1,2,3\}\times \{1,2,4\}$

$=\left\{\right(1,1),(1,2),(1,4),(2,1),(2,2),(2,4),(3,1),(3,2),(3,4\left)\right\}$

Hence, we represent B on the horizontal line and A on vertical line.

Graphical representation of $B\times A$ is as shown below :

(iii) We have,

$A=\{1,2,4\}$

$\therefore A\times A=\{1,2,4\}\times \{1,2,4\}$

$=\left\{\right(1,1),(1,2),(1,4),(2,1),(2,2),(2,4),(4,1),(4,2),(4,4\left)\right\}$

Graphical representation of $A\times A$ is shown below :

(iv) We have,

$B=\{1,2,3\}$

$B\times B=\{1,2,3\}\times \{1,2,3\}$

$=\left\{\right(1,1),(1,2),(1,3),(2,1),(2,2),(2,3),(3,1),(3,2),(3,3\left)\right\}$

Graphical representation of $B\times B$ is shown below :