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Use the laws of logic to show that ((s V ¬r V¬q) ^ (¬s V r V s) ^ (¬r v¬s V¬q)) = ¬(q^r).

Use the laws of logic to show that ((s V ¬r V¬q) ^ (¬s V r V s) ^ (¬r v¬s V¬q)) = ¬(q^r).

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 Mathematica. Laws of logic. Can you show me step-by-step how to solve prove this using the laws of logic. The steps should look just like the example I provided. Please upload your own work. I will rate your work. Thanks!
2. (15) Use the laws of logic to show that ((s VrV¬r)^(-s VrVq) ^ (rV¬s Vq)) =qv¬s. 5 points for a proof in good form. 5 points for getting there, particularly realizing that distribution and domination are the keys. 5 points for justifications. Do not deduct for omitting commutativity or associativity steps or justifications. Do deduct for omitting distribution, negation or domination steps or justifications. Alternate paths that successfully get to the end get full credit. (s VrV¬r) A (s VrVq) ^ (rV¬s Vq) = (SVT) ^ (¬s VrVq) ^ (r Vs V q) = (sv¬rVq) ^ (rv¬svq) = (qv¬s V¬r) ^ (qV¬s Vr) = ((q v¬s) v¬r)^((qV¬s) Vr) = (q v¬s) ^ (¬r Vr) = (qV¬s) ^ T = (q v¬s) negation domination comm assoc dist negation domination
Transcribed Image Text:2. (15) Use the laws of logic to show that ((s VrV¬r)^(-s VrVq) ^ (rV¬s Vq)) =qv¬s. 5 points for a proof in good form. 5 points for getting there, particularly realizing that distribution and domination are the keys. 5 points for justifications. Do not deduct for omitting commutativity or associativity steps or justifications. Do deduct for omitting distribution, negation or domination steps or justifications. Alternate paths that successfully get to the end get full credit. (s VrV¬r) A (s VrVq) ^ (rV¬s Vq) = (SVT) ^ (¬s VrVq) ^ (r Vs V q) = (sv¬rVq) ^ (rv¬svq) = (qv¬s V¬r) ^ (qV¬s Vr) = ((q v¬s) v¬r)^((qV¬s) Vr) = (q v¬s) ^ (¬r Vr) = (qV¬s) ^ T = (q v¬s) negation domination comm assoc dist negation domination
Use the laws of logic to show that ((s V ¬r V ¬q) ^ (¬s V r V s) ^ (¬r V ¬s V¬q)) = ¬(q ^r).
Transcribed Image Text:Use the laws of logic to show that ((s V ¬r V ¬q) ^ (¬s V r V s) ^ (¬r V ¬s V¬q)) = ¬(q ^r).
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