2. Consider the following formula (represented as strings): (i) p^-qpV (p→q) (ii) pV¬q→ p^q (a) Add parentheses to each of the formulas to clarify their meaning, e.g. p^-q Vr means (p^(-q)) V r. (b) Make a truth table for each of the formulas. (c) For each formula, use your truth table from (b) to determine whether the formula is satisfiable, valid, unsatisfiable, and/or invalid. If the formula is satisfiable, identify an interpretation for which v(A) = T. If the formula is invalid, identify an interpretation for which v (A) = F. (Note: To identify an interpretation, it suffices to indicate the truth values the interpre- tation assigns to each atom appearing in the formula.)
2. Consider the following formula (represented as strings): (i) p^-qpV (p→q) (ii) pV¬q→ p^q (a) Add parentheses to each of the formulas to clarify their meaning, e.g. p^-q Vr means (p^(-q)) V r. (b) Make a truth table for each of the formulas. (c) For each formula, use your truth table from (b) to determine whether the formula is satisfiable, valid, unsatisfiable, and/or invalid. If the formula is satisfiable, identify an interpretation for which v(A) = T. If the formula is invalid, identify an interpretation for which v (A) = F. (Note: To identify an interpretation, it suffices to indicate the truth values the interpre- tation assigns to each atom appearing in the formula.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:2. Consider the following formula (represented as strings):
(i) p^-qpV (p→q)
(ii) p V-q→-p^q
(a) Add parentheses to each of the formulas to clarify their meaning, e.g. p^-q Vr means
(p^(-q)) V T.
(b) Make a truth table for each of the formulas.
(c) For each formula, use your truth table from (b) to determine whether the formula is
satisfiable, valid, unsatisfiable, and/or invalid. If the formula is satisfiable, identify an
interpretation for which us (A) = T. If the formula is invalid, identify an interpretation
for which v(A) = F.
(Note: To identify an interpretation, it suffices to indicate the truth values the interpre-
tation assigns to each atom appearing in the formula.)
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