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Simplify ¬(s∧(q∨¬s)) to ¬s∨¬q

Simplify ¬(s∧(q∨¬s)) to ¬s∨¬q

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Answer #1

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¬(s∧(q∨¬s)) to ¬s∨¬q

= ¬((s∧q) v (s∧¬s)) ( From distributive rule: p ∧ (q ∨ r) = (p ∧ q) ∨ (p ∧ r))

= ¬((s∧q) v F) ( From contradiction rule p ∧ ¬p = F)

= ¬(s∧q) ( From or simplification rule p ∨ F = p)

= ¬s v ¬q ( From demorgan law: ¬(p ∨ q) = ¬p ∧ ¬q)

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