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(a) Find a similar sequence of equivalences that proves (pV (qVr)) V s = p V (qV (r V s)). (b) The expression p^q^r^s can be parenthesized in 5 different ways. Four of these ways are listed in either the example above or part (a), what is the fifth way to parenthesize p^q^r^s? (c) Use logical equivalences to show that your expression in (b) is equivalent to one of the expressions in (a).

(a) Find a similar sequence of equivalences that proves (pV (qVr)) V s = p V (qV (r V s)). (b) The expression p^q^r^s can be parenthesized in 5 different ways. Four of these ways are listed in either the example above or part (a), what is the fifth way to parenthesize p^q^r^s? (c) Use logical equivalences to show that your expression in (b) is equivalent to one of the expressions in (a).

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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(a) Find a similar sequence of equivalences that proves (pv (qVr)) Vs = p V (qV (r Vs)). (b) The expression p^q^r^s can be parenthesized in 5 different ways. Four of these ways are listed in either the example above or part (a), what is the fifth way to parenthesize p^q^r^s? (c) Use logical equivalences to show that your expression in (b) is equivalent to one of the expressions in (a).
Transcribed Image Text:(a) Find a similar sequence of equivalences that proves (pv (qVr)) Vs = p V (qV (r Vs)). (b) The expression p^q^r^s can be parenthesized in 5 different ways. Four of these ways are listed in either the example above or part (a), what is the fifth way to parenthesize p^q^r^s? (c) Use logical equivalences to show that your expression in (b) is equivalent to one of the expressions in (a).
Q. B3: a) The logical expression (pv(qvr))vs = (pvt)vs = pv(tvs) So, (pv(qvr))vs = pv((qvr)vs) = pv(qv(rvs)) b) by substitution of t = q v r by the associative law for v by substitution of q V r = t by the associative law for v The 5 different easy the expression p^q^r^s can be parenthesized are: 1. (p^(q^(r^s))) 2. ((p^q)^(r^s)) 3. (p^q)^(r^s) 4. (p^(q^r))^s 5. p^((q^r)^s)
Transcribed Image Text:Q. B3: a) The logical expression (pv(qvr))vs = (pvt)vs = pv(tvs) So, (pv(qvr))vs = pv((qvr)vs) = pv(qv(rvs)) b) by substitution of t = q v r by the associative law for v by substitution of q V r = t by the associative law for v The 5 different easy the expression p^q^r^s can be parenthesized are: 1. (p^(q^(r^s))) 2. ((p^q)^(r^s)) 3. (p^q)^(r^s) 4. (p^(q^r))^s 5. p^((q^r)^s)
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