Section 1.5
Basic Proof Methods II
PROOF:
A PROOF BY CONTRADICTION:
To proof a statement P is true, we assume P is false. That is we
assume ~P is true. Then we get Q and ~Q
Which is a contradiction. Hence, ~P is false and P must be true.
Proof:
Example: Prove that x is odd iff x+1 is even
Proof:
x is odd
iff
x  2k  1
for some integer k
iff
x  1  (2k  1)  1
for some integer k
iff
x  1  2(k  1)
for some integer k  1
iff
x  1 is even