What equivalence/law was applied?[(p v q) ^ (p → r) ^ (q → r)] → r = ¬[(p v q) ^ (p → r) ^ (q → r)] v rO De Morgan's lawcommutativity and associativityassociativity and an idempotent lawO conditional-disjunction equivalence

We will find out the required law.

Answered: What equivalence/law was applied? [(p v…

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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prove in words: If {X, Y, Z} ` A ∧ ¬A, then {Y, Z} ` ¬X ` = derivability
Q2 Properties of the disjunction operator: (V) Jai 5laala Let p, q and r are three propositions. Using the truth table, show that: 1. pv q =q v p(J+yi la) (H. W) 2. (p V q) v r=p v (q V r) ( ) 3. pVp p(sll ) (H. W) 4. pVT=T (Domination Law) (H. W) 5. pVF= F (Identity Law) (H. W) 6. pv - p= T (H. W)
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Using the logical equivalences proven in class show that ¬(p v q v r) =¬p IL v bL Using the logical equivalences proven in class show that ((p v q) ^¬g) → p is a tautology (is always true).
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Let x, y, z ∈ { 0, 1 } be bits, and let ϕ be the logical expression ϕ(x,y,z) = (x ⇒ y) AND ((y AND z) ⇒ x). for which combinations of ϕ(x,y,z) is ϕ true(i.e 1)? Example: ϕ(1,1,1) is a combination of ϕ(x,y,z)
A logical equivalence is derived from Theorem 2.1.1. Supply a reason for each step.

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What equivalence/law was applied? [(p v q) ^ (p → r) ^ (q → r)] → r = ¬[(p v q) ^ (p → r) ^ (q → r)] v r O De Morgan's law commutativity and associativity associativity and an idempotent law O conditional-disjunction equivalence