How would you go about proving these:

1)

For all integers n, n is even if and only if n -1 is odd

2)

if d|(a+b) and d|a, where a,b and d are integers, d is not equal to 0

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- January 15th 2013, 06:53 AMmatrix37696How to prove an IFF (If and only If) statement!
How would you go about proving these:

1)

For all integers n, n is even if and only if n -1 is odd

2)

if d|(a+b) and d|a, where a,b and d are integers, d is not equal to 0 - January 15th 2013, 07:49 AMibduttRe: How to prove an IFF (If and only If) statement!
Suppose n is even then n = 2m for some m.

therefore n = 2m

obviously n-1=2m - 1 is odd

Alternatively

if n- 1 is odd then (n-1) + 1 = is n which is even for n-1 is odd.

we can also say that for n-1 being odd implies em-1 is odd where n = 2m for some m.

thus (n-1) = (2m-1)-1 = 2m-2 = 2(m-1) which is even.

Hence the proof