Question

If $A=\{1,2,3,4\}$ and ‘R’ be the relation on ‘A’ defined by {$\{(a,b):a,b\in A,axb$is an even number} ,then find the range of ‘R’.

• A. $\{2,4\}$
• B. $\{2,3,4\}$
• C. $\{1,2,4\}$
• D. All of the above

Answer 1

The correct option is D

All of the above

Explanation for correct option:

Finding range :

Given,$A=\{,2,3,4\}$

On verifying with the given options,

$\begin{array}{rcl}\{1,2,4\}\Rightarrow 1,2,4& \in & A\\ 1\times 2& =& 2\\ 1\times 4& =& 4\\ 2\times 4& =& 8\end{array}$

They are even.

$\begin{array}{rcl}\{2,4\}\Rightarrow 2,4& \in & A\\ 2\times 4& =& 8\left(even\right)\\ \{2,3,4\}\Rightarrow 2,3,4& \in & A\\ 2\times 3& =& 6\\ 3\times 4& =& 12\\ 2\times 4& =& 8\end{array}$

They are even.

All satisfy the given condition

Hence, correct option is $\left(D\right)$.