A set A has 5 elements and $\mathrm{B}=\{\mathrm{a}, \mathrm{b}, \mathrm{c}\}$. If the number of ele

Question

A set A has 5 elements and $\mathrm{B}=\{\mathrm{a}, \mathrm{b}, \mathrm{c}\}$. If the number of elements in $(\mathrm{A} 	imes \mathrm{B}) \cup(\mathrm{B} 	imes \mathrm{A})$ is n then

Professor PC Thomas Classes · Answer

If $\mathrm{A}, \mathrm{B}$ are disjoint $(\mathrm{A} 	imes \mathrm{B}) \cup(\mathrm{B} 	imes \mathrm{A})$ contains 30 elements. If $\mathrm{A} \supset \mathrm{B}$ then $\mathrm{B} 	imes \mathrm{B}$ is common to $\mathrm{A} 	imes \mathrm{B}$ and $\mathrm{B} 	imes \mathrm{A}$. \ $ \begin{aligned} & 	herefore(A 	imes B) \cup(B 	imes A) 	ext { contains } \ & 15+15-9=21 	ext { elements. } \ & 	herefore 21 \leq n \leq 30 \end{aligned} $