EXERCISE 1.13.3: Show an argument with quantified statements is invalid.Show that the given argument is invalid by giving values for the predicates P and Q over the domain (a, b).(a)x (P(x) → Q(x))3x - P(x):: 3x -Q(x)3x (P(x) v Q(x))3x -Q(x):: 3x P(x)~Feedback?

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Answered: EXERCISE 1.13.3: Show an argument with…

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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2. Use your own predicates P(x) and Q(x) to explain why (3r, P(x)) ^ (3x, Q(x)) is not logically equivalent to 3r, (P(x) A Q(x)).
Let P(x, y) be "x has taken class y," and Q(x, y) be "x has passed class y" and M(y) be "y is a math class," where the domain of x consists of all students in your class and the domain of y consists of all classes at LU. Use quantifiers to express this statement. (Assume that all email messages that were sent are received.) Every student in your class has passed a class at Liberty University that is not a math class.
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 True O False
6. Use the rules of inference from the formula sheet to show the follow argument is valid: Vx Q(x) 3x (P(x) v Q(x))
Show by example that these three statements are generally false:(a) A and AT have the same nullspace.(b) A and AT have the same free variables.(c) If R is the reduced form rref(A) then RT is rref(AT ).
Use the rules of inference to show that if 3x(M(x) AP(x)) and Vx(K (x) → ¬M(x)) are true, then 3x(P(x) ^ ¬K(x)) is also true, where the domains of all the quantifiers are the same.
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EXERCISE 1.13.3: Show an argument with quantified statements is invalid. Show that the given argument is invalid by giving values for the predicates P and Q over the domain (a, b). (a) (P(x) → Q(x)) 3x - P(x) :3x-Q(x) 3x (P(x) v Q(x)) 3x -Q(x) :: 3x P(x)