Answer:
The proving statements in the given choices should be:
If n is an integer such that n is divisible by 7, then n² is divisible by 7.
If n is an integer such that n is not divisible b 7, then n² is not divisible by 7
Step-by-step explanation:
- The statement to be proved is "An integer n is divisible by 7 if an only if n² is divisible by 7"
- The statement can be divided into two individual statements as
- A = An integer n is divisible by 7
- B = An integer n² is divisible by 7
- Thus the statements to be connected by the relation "If and only if" or implications from both sides.
- In notation we need to prove A <=> B
- To prove A <=> B need to satisfy two implications:
- A => B and B => A
- None of the given statements are directly from A => B and B => A thus test whether any combination results in A => B and B => A
The first choice is as follows:
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