7. Let P(x) be the propositional function "x>2" .The domain of discourse of the propositionalfunction P(x) is {1,2,3).The truth value of the proposition VxP(x) is

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Answered: 7. Let P(x) be the propositional…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 10CT: Statement P and Q are true while R is a false statement. Classify as true or false:...

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Statement P and Q are true while R is a false statement. Classify as true or false: a)PorQb)(PandQ)orR
let P and Q be predicates on some domain of discourse D and define p = Vx (P(x)) → Vx (Q(x)) q = Vx ( P(x) → Q(x) ). Check all statements that must be true. O If q is true, then p is true. None of the other choices. If p is true, then q is true.
(d) Let P(x) be the statement “ x² > 1 " and Q(x) be the statement "x+1 < 4". The universe of discourse consists of all real numbers. What are the truth values for the following: i. Væ(P(x) → Q(x)) ii. Jx(P(x) → Q(x)) iii. Vr(P(x) A Q(x)) iv. 3x(P(x) A -Q(x))
Suppose the domain of the propositional function p(x) consists of the integers -2, -1, 0, 1, and 2. Write the following proposition using disjunctions, conjunctions, and negations. Vx-p(x)
Suppose P(x) is some predicate for which the statement ∀xP(x) is true. Is it also the case that ∃xP(x) is true? In other words, is the statement ∀xP(x) → ∃xP(x) always true? Is the converse always true? Assume the domain of discourse is non-empty. Explain.
Suppose that Q(x) is the statement "x +1 = 2x," and the universe of discourse is R. (a) What is the truth value of VxQ(x)? Explain your answer. (b) What is the truth value of 3xQ(x)? Explain your answer.
Let Q(x) be the statement "x + 1 > 2x." If the universe of discourse consists of all integers, which of these predicates will be true? A) vx ¬Q(x) Vx Q(x) c) Q(-1) D) Q(1)
Let P(x) be the predicate, “5x + 1 is even." a. Is P(15) true or false?? b. What, if anything, can you conclude about 3xP(x) from the truth value of P(15)? OP(x) must be true. ³xP(x) must be false. OP(x) could be true or could be false. c. What, if anything, can you conclude about VxP(x) from the truth value of P(15)? OVxP(x) must be true. OVxP(x) must be false. OVxP(x) could be true or could be false.
part D E F
Let P (x) be the statement “ x2 > 1 ” and Q(x) be the statement “x+1 < 4”.The universe of discourse consists of all real numbers. What are the truthvalues for the following:i. ∀x(P (x) →Q(x))ii. ∃x(P (x) →Q(x))iii. ∀x(P (x) ∧Q(x))iv. ∃x(P (x) ∧¬Q(x))
3. Determine the truth value of each of these statements. The domain for every variable is the set of all real numbers. You do not need to justify your answers. (a) ³x³y(x² + y² 1) (k) 3x0 Vy(xy > 1)
The predicate P and Q are defined as: Q(x, y): (x+y)/2=4, P(x, y, z)=(x+y)/2= z The domain for all the variables is the set of real numbers. Select the proposition that is false. O a. Q(4,4) O b. P(0, 2, 2) O c. Q(0,8) O d. P(-2, 2, 0)

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7. Let P(x) be the propositional function "x>2" .The domain of discourse of the propositional function P(x) is {1,2,3). The truth value of the proposition VxP(x) is