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Let P be the set consisting of the names of logical equivalences from Table 6 of section 1.3.2. Let S be the set consisting of the names of logical equivalences from Table 1 of section 2.2.2. (a) Use the roster method to list S - P. Note: You do not need to submit P or S, just S P. (b) What is the value of P - S? (c) What is the value of |P| — |S|.

Let P be the set consisting of the names of logical equivalences from Table 6 of section 1.3.2. Let S be the set consisting of the names of logical equivalences from Table 1 of section 2.2.2. (a) Use the roster method to list S - P. Note: You do not need to submit P or S, just S P. (b) What is the value of P - S? (c) What is the value of |P| — |S|.

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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Let P be the set consisting of the names of logical equivalences from Table 6 of section 1.3.2. Let S be the set consisting of the names of logical equivalences from Table 1 of section 2.2.2. (a) Use the roster method to list S – P. Note: You do not need to submit P or S, just S – P. (b) What is the value of P - S? (c) What is the value of |P| — |S|.
Transcribed Image Text:Let P be the set consisting of the names of logical equivalences from Table 6 of section 1.3.2. Let S be the set consisting of the names of logical equivalences from Table 1 of section 2.2.2. (a) Use the roster method to list S – P. Note: You do not need to submit P or S, just S – P. (b) What is the value of P - S? (c) What is the value of |P| — |S|.
TABLE 6 Logical Equivalences. Equivalence P^T = P pvF = p pv T = T PAF = F pvp = p PAP=p -(-p) = p pvqqvp p^q=q^p (pvq) vr=pv (qV r) (p^q) ^r=p^ (q^r) pv (q^r) = (pVq) ^ (p Vr) p^ (qvr) = (p^q) v (p^r) (p^q) =pV¬q (pv q) = p ^ q PV (p^q) = p p^(pvq) = p PV-P = T PAP=F Name Identity laws Domination laws Idempotent laws Double negation law Commutative laws Associative laws Distributive laws De Morgan's laws Absorption laws Negation laws TABLE 1 Set Identities. Identity An U=A AUØ = A AUU = U And=0 AUA = A AnA = A (A) = A AUB=BUA AnB=BnA AU (BUC) = (AUB) UC An (BnC) = (AnB) nC AU (BNC) = (AUB) n(AUC) An (BUC) = (AnB) u (An C) ANB=AUB AUB=ANB AU (ANB) = A An (AUB) = A AUĀ= U ANĀ=Ø Name Identity laws Domination laws Idempotent laws Complementation law Commutative laws Associative laws Distributive laws De Morgan's laws Absorption laws Complement laws
Transcribed Image Text:TABLE 6 Logical Equivalences. Equivalence P^T = P pvF = p pv T = T PAF = F pvp = p PAP=p -(-p) = p pvqqvp p^q=q^p (pvq) vr=pv (qV r) (p^q) ^r=p^ (q^r) pv (q^r) = (pVq) ^ (p Vr) p^ (qvr) = (p^q) v (p^r) (p^q) =pV¬q (pv q) = p ^ q PV (p^q) = p p^(pvq) = p PV-P = T PAP=F Name Identity laws Domination laws Idempotent laws Double negation law Commutative laws Associative laws Distributive laws De Morgan's laws Absorption laws Negation laws TABLE 1 Set Identities. Identity An U=A AUØ = A AUU = U And=0 AUA = A AnA = A (A) = A AUB=BUA AnB=BnA AU (BUC) = (AUB) UC An (BnC) = (AnB) nC AU (BNC) = (AUB) n(AUC) An (BUC) = (AnB) u (An C) ANB=AUB AUB=ANB AU (ANB) = A An (AUB) = A AUĀ= U ANĀ=Ø Name Identity laws Domination laws Idempotent laws Complementation law Commutative laws Associative laws Distributive laws De Morgan's laws Absorption laws Complement laws
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