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In this topic we look at how to prove that something is ALWAYS TRUE - so simply giving an example is not sufficient

Prove that "even + even = even"

2a + 2b            this could represent any "even + even" if a and b are integers

=2(a+b)            twice any integer is always even and (a+b) is an integer hence the original statement is always true



Prove that "odd2 = odd"

2n                n is an integer and twice any integer is always even

2n + 1          must be odd since "even + odd = odd"

(2n + 1)2      now we square our odd number

= 4n2 + 4n + 1

=2 (2n2 + 2n) +1    this is an odd number since 2(integer) + 1 is always odd

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