Answer:
The correct counterexample is [tex]b \leq 6[/tex].
Step-by-step explanation:
We proceed to demonstrate the validity of given implication by direct demonstration and use of our knowledge in algebra:
1) [tex]a + b \leq 8[/tex] Given.
2) [tex]a = 2[/tex] Given.
3) [tex]2+b \leq 8[/tex] 2) in 1)
4) [tex]2 + b +(-2) \leq 8 +(-2)[/tex] Compatibility with addition.
5) [tex]b+[2+(-2)]\leq 6[/tex] Commutative and associative properties/Definition of subtraction
6) [tex]b \leq 6[/tex] Existence of additive inverse/Modulative property/Result.
This contradicts what implies the given proposition. The correct counterexample is [tex]b \leq 6[/tex].
