Logic: How can I prove these …?

How can I prove these without truth tables.

a) (( A-> B ) -> A) => A

b) ( ( A and ~B ) -> B) -> ( A-> B )

c) (A and ~B) <=> ~( A -> B )

If you could help even with one of them, and say how it was done, it would be helpful.

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Top 1 Answers

A few days ago

Danielle

Favorite Answer

ill give (c) a try

(A and NOT B) <=> NOT (A => B)

1. A AND NOT B HYPOTHESIS

2. A => B ASSUMPTION

3. NOT A => NOT B contrapositive law (theres a law)

4. NOT A ASSUMPTION

5. NOT B line 4,3 => Elimination

6. A => B ASSUMPTION

7. A ASSUMPTION

8. A line 7,6 => Elimination

9 NOT (A => B) lines 2-5,6-8, NOT introduction

Hope that helps

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