alleryStart learning →Which pattern fails in every possible case, whatever p stands for?
Ap ∨ ~ p
Bp ∨ q
Cp ∧ ~ p
Dp → p
Answer & Solution
Correct answer: C. p ∧ ~ p
p and ~ p can never both be true, so the conjunction is always false.
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The lamp in a parallel circuit of two switches is off only whenIn switching tests, the value 1 stands for a switch that isTwo switches wired side by side, in parallel, act likeTwo switches wired one after another, in series, act likeJoining any statement p with a tautology by 'or' always yieldsSimplify p ∨ (p ∧ q) using absorption:Rewriting 'p if and only if q' using implications givesRewriting an implication p → q using only ~ and ∨ gives