Example 1
Say we're trying to prove by contradiction that if n2 is an odd number, then n is also odd for all integers n. What's our proposition? What's our supposition?
Example 2
If our supposition in a proof by contradiction was "there exists some integer n such that the product of n and its reciprocal does not equal 1," what was our proposition?
Example 3
Prove the following statement by contradiction:
There is no integer solution to the equation x2 – 5 = 0.