# Homework Help: Using inference rules/equivalences

1. Dec 9, 2015

### Upeksha

1. The problem statement, all variables and given/known data
Using[/PLAIN] [Broken] inference rules/equivalencies, Show that
( ( (¬ A ∨ ¬ B ) → ( C ∧ D ) ) ∧ ( C → E) ∧ ( ¬ E )) → A

2. Relevant equations
( ( (¬ A ∨ ¬ B ) → ( C ∧ D ) ) ∧ ( C → E) ∧ ( ¬ E )) → A

3. The attempt at a solution

Using inference rules/equivalencies, Show that
( ( (¬ A ∨ ¬ B ) → ( C ∧ D ) ) ∧ ( C → E) ∧ ( ¬ E )) → A

( (¬ A ∨ ¬ B ) → ( C ∧ D ) ) ∧ ( C → E) ∧ ( ¬ E )
Then,
( (¬ A ∨ ¬ B ) → ( C ∧ D ) ) ∧ ¬ E
( ¬( A ∧ B ) → ( C ∧ D ) ) ∧ ¬ E
( ¬¬( A ∧ B ) ∨ ( C ∧ D ) ) ∧ ¬ E
( ( A ∧ B ) ∨ ( C ∧ D ) ) ∧ ¬ E
After that, I cannot reach the answer → A

Last edited by a moderator: May 7, 2017
2. Dec 9, 2015

### RUber

To make sure I am reading this right, I will use English connectors.
[ (not A or nor B ) implies (C and D) ] and [( C implies E ) and (not E) ].
The right side simplifies to (not C) and (not E), not just (not E) like you have.
Having the not C will help you conclude that A must be true.