Question

List the elements of $\mathit{B}\mathbf{\times }\mathit{C}$when $B\mathbf{=}\left\{a,b,c\right\}$and $\mathit{C}\mathbf{=}\left\{0,1,c\right\}$.

Short answer

The value of $B\times C$is $\left\{\left(a,0\right),\left(a,1\right),\left(a,c\right),\left(b,0\right),\left(b,1\right),\left(b,c\right),\left(c,0\right),\left(c,1\right),\left(c,c\right)\right\}$.

Step-by-step solution

Consider the given statement

The sets are$B=\left\{a,b,c\right\}$ and $C=\left\{0,1,c\right\}$.

Showing the elements of the sets  B×C

The value of $B\times C$can be listed as follows:

$\begin{array}{c}B\times C=\left\{a,b,c\right\}\times \left\{0,1,c\right\}\\ =\left\{\left(a,0\right),\left(a,1\right),\left(a,c\right),\left(b,0\right),\left(b,1\right),\left(b,c\right),\left(c,0\right),\left(c,1\right),\left(c,c\right)\right\}\end{array}$

Therefore, the value of$B\times C$ is $\left\{\left(a,0\right),\left(a,1\right),\left(a,c\right),\left(b,0\right),\left(b,1\right),\left(b,c\right),\left(c,0\right),\left(c,1\right),\left(c,c\right)\right\}$.