Using inference rules/equivalences

[Upeksha]

Homework Statement

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

Homework Equations

( ( (¬ A ∨ ¬ B ) → ( C ∧ D ) ) ∧ ( C → E) ∧ ( ¬ E )) → A[/B]

The Attempt at a Solution

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

This is my answer.
Consider about,
( (¬ 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

 

[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.