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
(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)
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.
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)
answer it correctly and asap please, thank you so much
132 #1
Let B(x) be the predicate "person x is a fan of the Bulldogs" and let y(x) be the predicate "person x is a fan of the Yellow Jackets," where the domain for the variable x is the set of all people. Express the following symbolic proposition as an English sentence: 3x(B(x) VY(x)) Some person is a fan of the Bulldogs or a fan of the Yellow Jackets. Every person is a fan of the Bulldogs or a fan of the Yellow Jackets. Some person is a fan of the Bulldogs and a fan of the Yellow Jackets. Every person is a fan of the Bulldogs and a fan of the Yellow Jackets.
The domain for this problem is some unspecified collection of numbers. Consider the predicate P(x, y) = "x is greater than y." (a) Translate the following statement into predicate logic. Every number has a number that is greater than it. (x)(3)(x, y) (x), x) (3x)(y), x) (x)(³)(y,x) Ⓒ (3x)(³y)P(y,x) (b) Negate your expression from part (a), and simplify it so that no quantifier or connective lies within the scope of a negation. O (3x)(3)(~P(y, x)) ((((, x)) (3x)(V)(P(x, y)) (3x)(V)(Py, x)) (x)(3)(Py, x)) (c) Translate your expression from part (b) into understandable English. Don't use variables in your English translatio O All numbers have a number that they are less than or equal to. O There is a number that has a number that it is less than or equal to. O There is a number that all numbers are greater than or equal to. O There is a number that all numbers are less than or equal to. O All numbers are less than or equal to all numbers.
STRICTLY HANDWRITTEN ANSWER. I DON'T NEED TYPEWRITTEN ANSWERS. HANDWRITTEN PLS!
2. Let P(x) be "x is a student in this class," Q(x) be “x knows how to write programs in Python," and R(x) be “x can get a good job," where the domain of x consists of all people. Write the following argument in argument form and use the rules of inference to show that the argument is valid. Tom is a student in this class. Tom knows how to write programs in Python. Everyone who knows how to write programs in Python can get a good job. Therefore, some student in this class can get a good job.

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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