Consider the logical formula (∀c)((∀x)(P(c,x,y)→P(c,y,x))→Q(c,z)). Don't try to make sense of it; it is a monstrosity. Simply answer: which of its variables are free?Group of answer choicescxyz Let E(x) be the predicate "x is even," T(x) be the predicate "x is divisible by 3," and F(x) be the predicate "x is divisible by 4." Check all true statements. (x has type natural number)Group of answer choices(∀x)(E(x) --> F(x))(∀x)(F(x) --> E(x))(∀x)(E(x) --> T(x))(∀x)(T(x) --> T(x))

Answered: Consider the logical formula…

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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Consider the logical formula (∀c)((∀x)(P(c,x,y)→P(c,y,x))→Q(c,z)). Don't try to make sense of it; it is a monstrosity. Simply answer: which of its variables are free?

Group of answer choices

Let E(x) be the predicate "x is even," T(x) be the predicate "x is divisible by 3," and F(x) be the predicate "x is divisible by 4." Check all true statements. (x has type natural number)

Group of answer choices

(∀x)(E(x) --> F(x))

(∀x)(F(x) --> E(x))

(∀x)(E(x) --> T(x))

(∀x)(T(x) --> T(x))

Expert Solution

Step 1

Variables which are in the scope of some quantifier are called bound variables. All other variables present in the expression are called free variables.

For given problem, c and x are bound variables since they are in scope of universal quantifier. Rest of the variables are free variables.

Thus, y and z are free variables.

Options C and D are correct.

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