I know De-Morgan's law that $$ -(p∧q) = -p∨-q $$(adsbygoogle = window.adsbygoogle || []).push({});

Also $$ -(p∨q) = -p∧-q $$

But for material implication and bi conditional operations there are also some transformation.

What is the law or proof for it? Like

$$ p⇒q = -p∨q $$

$$ p ↔q = (p∧q) ∨ (-p∧-q) $$

There may be other properties also that I don't know.

How one can derive or say that?

SideNote: Why PF don't have a negation ( tilda symbol) ?

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# Transformation rules in Boolean algebra

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