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.---**Note:** There are no graphs or diagrams associated with this question.

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Answered: Select the logical expression that is…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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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)))