Question

If a + b ≤ 8 and a = 2, then b ≤ 5.Which of the following would be a counterexample?

Answer 1

The correct counterexample is
`b \leq 6`.

Explanation:

We proceed to demonstrate the validity of given implication by direct demonstration and use of our knowledge in algebra:

1)
`a + b \leq 8` Given.

2)
`a = 2` Given.

3)
`2+b \leq 8` 2) in 1)

4)
`2 + b +(-2) \leq 8 +(-2)` Compatibility with addition.

5)
`b+[2+(-2)]\leq 6` Commutative and associative properties/Definition of subtraction

6)
`b \leq 6` Existence of additive inverse/Modulative property/Result.

This contradicts what implies the given proposition. The correct counterexample is
`b \leq 6`.