Question

Determine whether the statement is true or false. If false, provide a counterexample.

a) If a natural number is divisible by 7, then it must also be divisible by 21.

b) If a natural number is divisible by 7 and 5, then it must also be divisible by 35.

Answer 1

A false, for example 14
B true

Answer 2

why

Answer 3

for A I have given a counterexample
for B if a number is divisible of 7 and 5 than that number looks like this:
7*5*x =35*x so 35 is also a factor of that number

Answer 4

Or for A you can see that 21 is \(7\times 3\) In order for a number to be divisible by 7 it must have 7 as a factor, but to be divisible by 21 it must have 7, and 3 as factors. So any multiple of 7 which has no factor of 3 will not be divisible by 21.