Question

If $a, b$ and $c \in N$ which one of the following is not true ?

• A. $a \mid b$ and $a|c \Rightarrow a| b+c$
• B. $a|b+c \Rightarrow a| b$ and $a \mid c$
• C. $a \mid b$ and $b|c \Rightarrow a| c$
• D. $a \mid b$ and $a|c \Rightarrow a| 3 b+2 c$

Answer 1

Answer: (B)

$a|b+c \Rightarrow a| b$ and $a \mid c$

Answer 2

By taking option (b)
$a | b( + c) \nRightarrow a|b$ and $a|c$
e.g., $6 \, 18 \; \nRightarrow 6| 1$ and $6|17$