Select the logical expression that is equivalent to:-3x(Q(x)^(P(X)VS(x))) x(Q(x)vP(x)v(x)) (-Q(x)v(P(x)^S(x))) vx(-Q(x)v(P(x)vS(x))) (-Q(x)v-P(x)^-S(x)))
Select the logical expression that is equivalent to:-3x(Q(x)^(P(X)VS(x))) x(Q(x)vP(x)v(x)) (-Q(x)v(P(x)^S(x))) vx(-Q(x)v(P(x)vS(x))) (-Q(x)v-P(x)^-S(x)))
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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Question
Discrete mathematics
![**Logical Equivalence Exercise**
In this exercise, you'll select the logical expression that is equivalent to the given expression:
**Expression to analyze:**
\[
\forall x(Q(x) \rightarrow (\lnot P(x) \lor S(x)))
\]
**Select the equivalent logical expression from the options below:**
1. \(\forall x(Q(x) \lor [P(x) \rightarrow S(x)])\)
2. \(\forall x(Q(x) \lor (P(x) \lor S(x)))\)
3. \(\forall x(Q(x) \rightarrow (\lnot P(x) \land S(x)))\)
4. \(\forall x(Q(x) \rightarrow (P(x) \lor S(x)))\)
Choose the expression that maintains the logical equivalence through the appropriate use of logical operators and quantifiers. This exercise challenges your understanding of predicate logic and the manipulation of logical expressions.
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**Note:** There are no graphs or diagrams associated with this question.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffd14cb93-d503-4d54-908f-081a6b7caf80%2Ff5f77621-3cb5-45b1-a954-56134c8dbcb5%2Fjr2miwm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Logical Equivalence Exercise**
In this exercise, you'll select the logical expression that is equivalent to the given expression:
**Expression to analyze:**
\[
\forall x(Q(x) \rightarrow (\lnot P(x) \lor S(x)))
\]
**Select the equivalent logical expression from the options below:**
1. \(\forall x(Q(x) \lor [P(x) \rightarrow S(x)])\)
2. \(\forall x(Q(x) \lor (P(x) \lor S(x)))\)
3. \(\forall x(Q(x) \rightarrow (\lnot P(x) \land S(x)))\)
4. \(\forall x(Q(x) \rightarrow (P(x) \lor S(x)))\)
Choose the expression that maintains the logical equivalence through the appropriate use of logical operators and quantifiers. This exercise challenges your understanding of predicate logic and the manipulation of logical expressions.
---
**Note:** There are no graphs or diagrams associated with this question.
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