Must show all the work and use the 2nd image as reference if needed to. Either provide a counter example or prove using the algebra of sets:VA, B,C Cu(A\ (B\ProvenDisproven StatementPropertypV p =p p^p = ppvq = q v p pAq = q^pp V (q V r) = (p V q) V rp^ (q Ar) = (p ^ q) ArIdempotenceCommutativityAssociativityp V (q ^ r) = (p V q) ^ (p V r)p^ (q v r) = (p ^q) v (p ^ r)pv (p A q) = p p^ (p V q) = pp Vl= p p^T = pp V (¬p) = T p ^ (¬p) = 1pVT =T pAl= 1¬(¬p) = p1= (T)- T= (1)–¬(p v q) = (¬p) ^(¬q)¬(p Aq) = (¬p) v (¬q)DistributivityAbsorptivityIdentityComplementarityDominanceInvolutionExclusivityDeMorgan'sInferenceNameInferenceName(p) Ca)pnqAdjunctionSimplification(p V q) (¬q)DisjunctiveSyllogismpAdditionpvqp → (¬p)ApagogicalSyllogismReductio AdAbsurdum(p → q) (p)(p → q) (¬a)Modus PonensModus Tollens(p → q) (q → r)HypotheticalSyllogismConditionalizationp-r(p → q) (¬p →r)(p → q) (r → s)(p V r) → (q V s)(p → q) (p → r)p → (a Ar).ResolventComplex DilemmaqvrDilemma(p → q).(Gp → q).ExhaustiveCompositionalSvllogismSyllogismFallacyNameFallacyName(p → q) (q)Asserting theConclusion(p → q) (¬p)Denying thePremise(p → q) (p → r)(p → ¬q) (q → ¬p)(¬p) ^ (¬q)FalseNon-SequiturElimination(p # q) (q ± r)(p # r)FalseFalse TransitionReduction

Let A, B, C be three sets To Prove : (A \ ( B \ C ))=(( A \ B )∪(A ∩C )) Properties on sets: (1)…

Answered: Either provide a counter example or…

Math

Advanced Math

Either provide a counter example or prove using the algebra of sets: VA,B.C su(A\ (B \C) = (A \ B) U (A N C).

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.1: Postulates For The Integers (optional)

Problem 24E

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Question

Must show all the work and use the 2nd image as reference if needed to.

Either provide a counter example or prove using the algebra of sets:
VA, B,C Cu(A\ (B\
Proven
Disproven

Statement
Property
pV p =p p^p = p
pvq = q v p pAq = q^p
p V (q V r) = (p V q) V r
p^ (q Ar) = (p ^ q) Ar
Idempotence
Commutativity
Associativity
p V (q ^ r) = (p V q) ^ (p V r)
p^ (q v r) = (p ^q) v (p ^ r)
pv (p A q) = p p^ (p V q) = p
p Vl= p p^T = p
p V (¬p) = T p ^ (¬p) = 1
pVT =T pAl= 1
¬(¬p) = p
1= (T)- T= (1)–
¬(p v q) = (¬p) ^(¬q)
¬(p Aq) = (¬p) v (¬q)
Distributivity
Absorptivity
Identity
Complementarity
Dominance
Involution
Exclusivity
DeMorgan's
Inference
Name
Inference
Name
(p) Ca)
pnq
Adjunction
Simplification
(p V q) (¬q)
Disjunctive
Syllogism
p
Addition
pvq
p → (¬p)
Apagogical
Syllogism
Reductio Ad
Absurdum
(p → q) (p)
(p → q) (¬a)
Modus Ponens
Modus Tollens
(p → q) (q → r)
Hypothetical
Syllogism
Conditionalization
p-r
(p → q) (¬p →r)
(p → q) (r → s)
(p V r) → (q V s)
(p → q) (p → r)
p → (a Ar).
Resolvent
Complex Dilemma
qvr
Dilemma
(p → q).
(Gp → q).
Exhaustive
Compositional
Svllogism
Syllogism
Fallacy
Name
Fallacy
Name
(p → q) (q)
Asserting the
Conclusion
(p → q) (¬p)
Denying the
Premise
(p → q) (p → r)
(p → ¬q) (q → ¬p)
(¬p) ^ (¬q)
False
Non-Sequitur
Elimination
(p # q) (q ± r)
(p # r)
False
False Transition
Reduction

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