For statement given below, determine whether it is always true, s… - Vidyadip

Question

For statement given below, determine whether it is always true, sometimes true, or never true. Explain your answer. Mention examples and non-examples as appropriate. Justify your claim using algebra.
The sum of two even numbers is a multiple of 3.

✓

Answer

Let the two even numbers be $2 a+2 b$
$\text { Sum }=2 a+2 b=2(a+b)$
For $2(a+b)$ to be a multiple of $3,(a+b)$ must be multiple of 3 .
Example :
$2+4=6 \rightarrow \text { divisible by } 3$
$2+8=10 \rightarrow$ not divisible by 3
Conclusion : Sometimes true.

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