Either provide a counter example or prove using the algebra of sets: VA, B, C S U((A\ (B \ C) = (A \ B) U (A N C)). %| Proven Disproven Statement Property p V p = p p^ p = p pV q = q V p pAq=qp p V (q v r) = (p V q) vr p^(q ^ r) = (p ^ q) ^r pV (q ^ r) = (p V q) ^ (p V r) p^ (q v r) = (p ^q) v (p ^ r) p V (p ^ q) = p p^ (p V q) = p p V l= p_p^T = p p V (¬p) = T p ^ (¬p) = 1 pVT = T pAl= 1 ¬(-p) = p ¬(1) = T ¬(p V q) = (¬p) ^(¬q) ¬(p^q) = (¬p) v (¬q) Idempotence Commutativity Associativity Distributivity Absorptivity Identity Complementarity Dominance Involution ¬(T) = 1 Exclusivity DeMorgan's Inference Name Inference Name (p) (q) Adjunction Simplification (p V q) (¬q) Disjunctive Syllogism Addition p V q p → (¬p) Apagogical Syllogism Reductio Ad Absurdum (p → q) (p) (p → q) (¬q) Modus Ponens Modus Tollens (p → q) (q → r) p →r (p → q) (¬p → r) q V r Hypothetical Syllogism Conditionalization (p → q) (r → s) (p V r) → (q V s) (p → q) (p → r) p → (q Ar). Resolvent Complex Dilemma Dilemma (p → q) (¬p → q) Compositional Syllogism Exhaustive Syllogism Fallacy Name Fallacy Name (p → q) (g) Asserting the Conclusion (p → q) (¬p) Denying the Premise (p → ¬q) (q → ¬p) (¬p) ^ (¬9) False Elimination (p → q) (p → r) 9 →r Non-Sequitur (p # q) (q ± r) (p zr) False False Transition ¬p Reduction
Either provide a counter example or prove using the algebra of sets: VA, B, C S U((A\ (B \ C) = (A \ B) U (A N C)). %| Proven Disproven Statement Property p V p = p p^ p = p pV q = q V p pAq=qp p V (q v r) = (p V q) vr p^(q ^ r) = (p ^ q) ^r pV (q ^ r) = (p V q) ^ (p V r) p^ (q v r) = (p ^q) v (p ^ r) p V (p ^ q) = p p^ (p V q) = p p V l= p_p^T = p p V (¬p) = T p ^ (¬p) = 1 pVT = T pAl= 1 ¬(-p) = p ¬(1) = T ¬(p V q) = (¬p) ^(¬q) ¬(p^q) = (¬p) v (¬q) Idempotence Commutativity Associativity Distributivity Absorptivity Identity Complementarity Dominance Involution ¬(T) = 1 Exclusivity DeMorgan's Inference Name Inference Name (p) (q) Adjunction Simplification (p V q) (¬q) Disjunctive Syllogism Addition p V q p → (¬p) Apagogical Syllogism Reductio Ad Absurdum (p → q) (p) (p → q) (¬q) Modus Ponens Modus Tollens (p → q) (q → r) p →r (p → q) (¬p → r) q V r Hypothetical Syllogism Conditionalization (p → q) (r → s) (p V r) → (q V s) (p → q) (p → r) p → (q Ar). Resolvent Complex Dilemma Dilemma (p → q) (¬p → q) Compositional Syllogism Exhaustive Syllogism Fallacy Name Fallacy Name (p → q) (g) Asserting the Conclusion (p → q) (¬p) Denying the Premise (p → ¬q) (q → ¬p) (¬p) ^ (¬9) False Elimination (p → q) (p → r) 9 →r Non-Sequitur (p # q) (q ± r) (p zr) False False Transition ¬p Reduction
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Must show all the work....refer to the second image if needed to.
Transcribed Image Text:Either provide a counter example or prove using the algebra of sets:
VA, B, C S U((A\ (B \ C) = (A \ B) U (A N C)).
%|
Proven
Disproven
Transcribed Image Text:Statement
Property
p V p = p p^ p = p
pV q = q V p pAq=qp
p V (q v r) = (p V q) vr
p^(q ^ r) = (p ^ q) ^r
pV (q ^ r) = (p V q) ^ (p V r)
p^ (q v r) = (p ^q) v (p ^ r)
p V (p ^ q) = p p^ (p V q) = p
p V l= p_p^T = p
p V (¬p) = T p ^ (¬p) = 1
pVT = T pAl= 1
¬(-p) = p
¬(1) = T
¬(p V q) = (¬p) ^(¬q)
¬(p^q) = (¬p) v (¬q)
Idempotence
Commutativity
Associativity
Distributivity
Absorptivity
Identity
Complementarity
Dominance
Involution
¬(T) = 1
Exclusivity
DeMorgan's
Inference
Name
Inference
Name
(p) (q)
Adjunction
Simplification
(p V q) (¬q)
Disjunctive
Syllogism
Addition
p V q
p → (¬p)
Apagogical
Syllogism
Reductio Ad
Absurdum
(p → q) (p)
(p → q) (¬q)
Modus Ponens
Modus Tollens
(p → q) (q → r)
p →r
(p → q) (¬p → r)
q V r
Hypothetical
Syllogism
Conditionalization
(p → q) (r → s)
(p V r) → (q V s)
(p → q) (p → r)
p → (q Ar).
Resolvent
Complex Dilemma
Dilemma
(p → q) (¬p → q)
Compositional
Syllogism
Exhaustive
Syllogism
Fallacy
Name
Fallacy
Name
(p → q) (g)
Asserting the
Conclusion
(p → q) (¬p)
Denying the
Premise
(p → ¬q) (q → ¬p)
(¬p) ^ (¬9)
False
Elimination
(p → q) (p → r)
9 →r
Non-Sequitur
(p # q) (q ± r)
(p zr)
False
False Transition
¬p
Reduction
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