Question

Consider the following statements.

$1.If(a,1),(b,2)$and $(c,1)$ are in $A\times B$and $n\left(A\right)=3,n\left(B\right)=2,$then $A=\{a,b,c\}$and $B=\{1,2\}$

$2.IfA=\{1,2\}$ and $B=\{3,4\}$ then $A\times (B\cap Ø)$is equal to $A\times B.$

• A. Only$1$is true.
• B. Only $2$ is true.
• C. Both are true.
• D. Neither $1$nor $2$ is true.

Answer 1

The correct option is A

Only$1$is true.

Step 1. Check the statement 1.

Given $(a,1),(b,2)$ and $(c,1)$are in $A\times B.$

$n\left(A\right)=3,n\left(B\right)=2$

Then $A=\{a,b,c\},B=\{1,2\}$

$A\times B=\left\{\right(a,1),(a,2),(b,1),(b,2),(c,1),(c,2)\}$

Thus statement $1$ is true.

Step 2. Check the statement 2.

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

$\begin{array}{rcl}(B\cap Ø)& =& Ø\\ A\times (B\cap Ø)& =& A\times Ø=Ø\\ A\times B& \ne & A\times (B\cap Ø)\end{array}$

Thus statement $2$ is false.

Hence ,the correct option is A.