Maths · Relations, type of relations, equivalence relations
Consider the statement, if is divisible by 30 then is divisible by 2,3 and by 5
Consider the statement, if \( n \) is divisible by 30 then \( n \) is divisible by 2,3 and by 5 Which of the following statements is equivalent to this statement??
- A. If \( n \) is not divisible by 30 then \( n \) is divisible by 2 or divisible by 3 or divisible by 5
- B. If \( n \) is not divisible by 30 then \( n \) is not divisible by 2 or not divisible by 3 or not divisible by 5
- C. If \( n \) is divisible by 2 and divisible by 3 and divisible by 5 then \( n \) is divisible by 30
- D. If \( n \) is not divisible by 2 or not divisible by 3 or not divisible by 5 then \( n \) is not divisible by 30
Step-by-step solution
The original statement is "If n is divisible by 30 then n is divisible by 2, 3 and 5". Its contrapositive is logically equivalent: "If n is not divisible by 2 or not divisible by 3 or not divisible by 5, then n is not divisible by 30". Option D matches this contrapositive.
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