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Subject: Discrete Structures

1.Show, by the use of the truth table/matrix, that the statement (p ∨ q) ∨ [(¬p)∧ (¬q)] is a tautology.

2.Show that p ↔ q and (p ∧ q) ∨ (¬p ∧ ¬q) are logically equivalent
 
We can see that
In the table 1 :- all entries in the last column are True
Hence,
(p ∨ q) ∨ [(¬p)∧ (¬q)] is a Tautology

In table 2 :- The last two columns of table are identical that is same
Hence,
p q and (p ∧ q) ∨ (¬p ∧ ¬q) are logically equivalent
 

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