Help with discrete math question. Show the following Statement is true: Let n be an integer. If 5n+2 is odd, then n is odd.?
This is a proof by contrapositive.
- ?Lv 73 years agoFavourite answer
The contrapositive here is "If n is not odd, then 5n+2 is not odd."
If n is not odd, it is even; n = 2k, where k is some integer.
Then 5n+2 = 5(2k) + 2 = 10k + 2 = 2(5k+1). This is a multiple of 2, so 5n+2 is even. QED.
- The GnosticLv 73 years ago
Statement: If 5n + 2 is odd, then n is odd.
Contrapositive: If n is even, then 5n + 2 is even.
If a statement is true, its contrapositive is true, and vice versa.
If n is even, then multiplying is by any integer will produce an even number.
If an even number (like 2) is added to an even number, the result is an even number.
Thus: if n is even, then (even number [5n]) + (even number ) = even number.
Contrapositive proven true.
Statement proven true.