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Example If we define t to be the compound proposition p V q, then we can see that ((pVq) Vr) Vs = (t Vr) Vs = tv (r Vs) = (pVg) V (r Vs) by substitution of t = p V q by the associative law for V by substitution of p V q = t Note: We may not always make the t substitutions explicit. With practice, we will become comfortable summarizing the above derivation as: ((pVg) Vr) Vs= (pVg) V (rVs) by the associative law applied to p V q, r, and s. (a) Find a similar sequence of equivalences that proves (p V (qVr)) Vs = p V (qV (r Vs)).

Example If we define t to be the compound proposition p V q, then we can see that ((pVq) Vr) Vs = (t Vr) Vs = tv (r Vs) = (pVg) V (r Vs) by substitution of t = p V q by the associative law for V by substitution of p V q = t Note: We may not always make the t substitutions explicit. With practice, we will become comfortable summarizing the above derivation as: ((pVg) Vr) Vs= (pVg) V (rVs) by the associative law applied to p V q, r, and s. (a) Find a similar sequence of equivalences that proves (p V (qVr)) Vs = p V (qV (r Vs)).

Advanced Engineering Mathematics
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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discrete math

Example If we define t to be the compound proposition p V q, then we can see that ((pVq) Vr) Vs = (t Vr) Vs = tv (r Vs) = (pVg) V (r Vs) by substitution of t = p V q by the associative law for V by substitution of p V q = t Note: We may not always make the t substitutions explicit. With practice, we will become comfortable summarizing the above derivation as: ((pVg) Vr) Vs= (pVg) V (rVs) by the associative law applied to p V q, r, and s. (a) Find a similar sequence of equivalences that proves (p V (qVr)) Vs = p V (qV (r Vs)).
Transcribed Image Text:Example If we define t to be the compound proposition p V q, then we can see that ((pVq) Vr) Vs = (t Vr) Vs = tv (r Vs) = (pVg) V (r Vs) by substitution of t = p V q by the associative law for V by substitution of p V q = t Note: We may not always make the t substitutions explicit. With practice, we will become comfortable summarizing the above derivation as: ((pVg) Vr) Vs= (pVg) V (rVs) by the associative law applied to p V q, r, and s. (a) Find a similar sequence of equivalences that proves (p V (qVr)) Vs = p V (qV (r Vs)).
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