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Subject: Discrete Structures

1.Show, by the use of the truth table/matrix, that the statement (p โˆจ q) โˆจ [(ยฌp)โˆง (ยฌq)] is a tautology.

2.Show that p โ†” q and (p โˆง q) โˆจ (ยฌp โˆง ยฌq) are logically equivalent
 
We can see that
In the table 1 :- all entries in the last column are True
Hence,
(p โˆจ q) โˆจ [(ยฌp)โˆง (ยฌq)] is a Tautology

In table 2 :- The last two columns of table are identical that is same
Hence,
p โ†” q and (p โˆง q) โˆจ (ยฌp โˆง ยฌq) are logically equivalent
 
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