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AUB=An B.

AUB=An B.

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 math: please write all laws which will you use to solve this. I have also attached the example please take a look at this. Thank you!

Problem 1 Let A and B be any given sets. Use set builder notation and logical equivalences to show that AUB=AN B.
Transcribed Image Text:Problem 1 Let A and B be any given sets. Use set builder notation and logical equivalences to show that AUB=AN B.
TABLE 6 Logical Equivalences. Equivalence PAT P PVF p PVT T PAF F pvp p PAP p pvqqvp PAq=qAp (pvq) vr (PA)Ar pv (qvr) p^(q^r) PV (q Ar) (pvq)^(pvr) PA(qVr) (PAq) v (p^r) p^q)p (pvq)=pAny pv (p^q) = p. PA(pvq) p PV-P=T Name Identity laws Domination laws Idempotent laws Double negation law Commutative laws Associative laws Distributive laws De Morgan's laws Absorption laws Negation laws Conditional Statements pqp Vq Definition of implication p-qq-p Contrapositive pq=(pq) ^ (q→ p) Definition of biconditional These 2 laws allow us to write multiple conjunctions (or disjunctions) in any order without parenthesis, i.e. pvqvr qvpVr PAqAr=rAp^q We already proved the first De Morgan's law
Transcribed Image Text:TABLE 6 Logical Equivalences. Equivalence PAT P PVF p PVT T PAF F pvp p PAP p pvqqvp PAq=qAp (pvq) vr (PA)Ar pv (qvr) p^(q^r) PV (q Ar) (pvq)^(pvr) PA(qVr) (PAq) v (p^r) p^q)p (pvq)=pAny pv (p^q) = p. PA(pvq) p PV-P=T Name Identity laws Domination laws Idempotent laws Double negation law Commutative laws Associative laws Distributive laws De Morgan's laws Absorption laws Negation laws Conditional Statements pqp Vq Definition of implication p-qq-p Contrapositive pq=(pq) ^ (q→ p) Definition of biconditional These 2 laws allow us to write multiple conjunctions (or disjunctions) in any order without parenthesis, i.e. pvqvr qvpVr PAqAr=rAp^q We already proved the first De Morgan's law
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