Question
Download Solution PDFThe logical statement [~(~p ∨ q) ∨ (p ∧ r)] ∧ (~q ∧ r) is equivalent to:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFLogical statement given is,
[~(~p ∨ q) ∨ (p ∧ r)] ∧ (~q ∧ r)
⇒ [(p ∧ ~q) ∨ (p ∧ r)] ∧ (~q ∧ r)
⇒ [(p ∧ ~q) ∧ (~q ∧ r)] ∨ [(p ∧ r) ∧ (~q ∧ r)]
⇒ [p ∧ ~q ∧ r] ∨ [p ∧ r ∧ ~q]
⇒ (p ∧ ~q) ∧ r
⇒ (p ∧ r) ∧ ~q
Hence, [~(~p ∨ q) ∨ (p ∧ r)] ∧ (~q ∧ r) = (p ∧ r) ∧ ~q
Last updated on Jul 11, 2025
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