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.
If two numbers are not divisible by 6, then their sum is not divisible by 6.

✓

Answer

Let the two numbers be $a$ and $b$.
Not divisible by 6 means they do not satisfy 6|a or 6|b.
But their sum can still be divisible by 6 .
Example : 2 and $4 \rightarrow$ both not divisible by 6 .
But, $2+4=6 \rightarrow$ divisible by 6 .
Conclusion : Sometimes true.

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