Check if the following statement is TRUE or FALSE.Let p(x) and g(x) be two open predicates in a universe of discourse. Is it true that (x) (p(x) v g(x)) is equivalent to(Vxp(x)) v (Vxq(x))?O TrueO False

We will check whether the given expressions are equivalent or not

Answered: Check if the following statement is…

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter4: Polynomial And Rational Functions

Section4.CT: Chapter Test

Problem 9CT

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1) Let I(x) be the statement “x has an Internet connection” and C(x, y) be the statement “x and y have chatted over the Internet,” where the domain for the variables x and y consists of all students in your class. Use quantifiers to express each of these statements. Jerry has an Internet Rachel has chatted over the Internet with Jan and Sharon have never chatted over the Everyone in the class has chatted with Sanjay has not chatted with everyone except Someone in your class does not have an Internet Not everyone in your class has an Internet Exactly one student in your class has an Internet Everyone except one student in your class has an Internet Everyone in your class with an Internet connection has chatted over the Internet with at least one other student in your Someone in your class has an Internet connection but has not chatted with anyone else in your There are two students in your class who have not chatted with each other over the There is a student in your class who has…
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Let C(x) be the statement "x has a cat," let D(x) be the statement "x has a dog," and let F(x) be the statement "x has a ferret." Express the statement "Some student in your class has a cat and a ferret, but not a dog." in terms of C(x), D(x), F(x), quantifiers, and logical connectives. Let the universe of discourse consist of all students in your class. A ax(C(x) ^ F(x)^¬D(x)) В -ax(C(x) A D(x) a F(x)). c) vx(C(x) v D(x) v F(x)) 3X(C(x) ^ D(x) ^ F(x))
Let I (x) be the statement "x has an Internet connection" and C(x, y) be the statement "x and y have chatted over the Internet," where the domain for the variables x and y consists of all students in your class. Use quantifiers to express "Everyone in your class with an Internet connection has chatted over the Internet with at least one other student in your class." A ) aXvy(x = y I(y)) В Vx(I(x) → ay(x = y ^ C(x, y)) 3x(1(x) ^ vy(x = y →¬C(x, y))) D axay(x = y n-C(x, y))
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Check if the following statement is TRUE or FALSE. Let p(x) and g(x) be two open predicates in a universe of discourse. Is it true that (x) (p(x) v g(x)) is equivalent to (Vxp(x)) v (Vxq(x))? True