Question

state laws of equivalence. write all the laws of equivalence.

Answer 1

Equivalence statements
Two statements are said to be equivalent if they have the same truth value.

Example
Following are two statements.
p = It is false that he is a singer or he is a dancer.
q = He is not a singer and he is not a dancer.

The first statement p consists of negation of two simple proposition
a = He is a singer.
b = He is a dancer.
They are connected by an OR operator (connective)
so we can write,
p = ~(a ∨ b)

The second statement q consists of two simple proposition
which are negation of a and b
~a = He is not a singer.
~b = He is not a dancer.
They are connected by an AND operator (connective)
so we can write,
q = ~a ∧ ~b

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