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.
A false, for example 14 B true
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
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.
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