The document discusses counterexamples and how they can disprove conjectures. It provides examples of conjectures like every rectangle being a square or if a>b and b=5 then a≥6 that are disproven through counterexamples, such as a rectangle that is not a square or a situation where a>b but a<6. It emphasizes that only one counterexample is needed to show a general statement is false.

1. Counterexamples

2. Conjecture:
The perimeter of a rectangle can never be an odd
number

3. Counterexample :
- an example that shows a general statement
to be false.
- it only takes one counterexample to prove
a conjecture false

4. Conjecture:
Every rectangle is a square.
Counterexample:

5. Conjecture:
If a>b and b=5, then a ≥ 6
Counterexample:

6. Students with low grade-point averages in high
school are invariably failures in life.

7. Exercise 48
Omit question 9