Question

Consider the following statements. Let $A=\{1,2,3,4\}$and $B=\{5,7,9\}$

$$\begin{gathered} 1.A\times B=B\times A \\ 2.n(A\times B)=n(B\times A) \end{gathered}$$

• A. Statement-1 is true.
• B. Statement-2 is true
• C. Both are true.
• D. Both are false.

Answer 1

The correct option is B

Statement-2 is true

Step 1. Check statement :

Given $A=\{1,2,3,4\},B=\{5,7,9\}$

$\begin{array}{rcl}A\times B& =& \left\{\right(1,5),(1,7),(1,9),(2,5),(2,7),(2,9),(3,5),(3,7),(3,9),(4,5),(4,7),(4,9\left)\right\}\\ B\times A& =& \left\{\right(5,1),(5,2),(5,3),(5,4),(7,1),(7,2),(7,3),(7,4),(9,1),(9,2),(9,3),(9,4)\}\\ A\times B& \ne & B\times A\end{array}$

Statement 1 is false.

Step 2. Check Statement 2:

$\begin{array}{rcl}n(A\times B)& =& n\left(A\right)\times n\left(B\right)=4\times 3=12\\ n(B\times A)& =& n\left(B\right)\times n\left(A\right)=3\times 4=12\\ n(A\times B)& =& n(B\times A)\end{array}$

Statement 2 is true.

Hence, the correct option is B.