Knowee
Questions
Features
Study Tools

Let the universe of discourse be the set of negative integers. By selecting True or False, give the truth value of the following:ForEvery x (| 2x + 1 | > 1).Question 9AnswerTrue False

Question

Let the universe of discourse be the set of negative integers. By selecting True or False, give the truth value of the following:ForEvery x (| 2x + 1 | > 1).Question 9AnswerTrue False

🧐 Not the exact question you are looking for?Go ask a question

Solution

To determine the truth value of the statement "ForEvery x (| 2x + 1 | > 1)" where the universe of discourse is the set of negative integers, follow these steps:

  1. Identify the universe of discourse: The set of negative integers {..., -3, -2, -1}.
  2. Analyze the expression inside the absolute value: 2x + 1.
  3. Evaluate the expression for different values of x in the set of negative integers.

Let's test a few values:

  • For x = -1: | 2(-1) + 1 | = | -2 + 1 | = | -1 | = 1.
  • For x = -2: | 2(-2) + 1 | = | -4 + 1 | = | -3 | = 3.
  • For x = -3: | 2(-3) + 1 | = | -6 + 1 | = | -5 | = 5.

From the above evaluations:

  • When x = -1, | 2x + 1 | = 1, which is not greater than 1.
  • When x = -2, | 2x + 1 | = 3, which is greater than 1.
  • When x = -3, | 2x + 1 | = 5, which is greater than 1.

Since there exists at least one value (x = -1) for which the expression | 2x + 1 | is not greater than 1, the statement "ForEvery x (| 2x + 1 | > 1)" is not true for all x in the set of negative integers.

Answer: False

This problem has been solved

Similar Questions

Let the universe of discourse be the set of positive integers. By selecting True or False, give the truth value of the following:ThereExistsUnique x (x = 2x + 1).Question 15AnswerTrueFalse

Let the universe of discourse be the set of negative integers. By selecting True or False, give the truth value of the following:ThereExistsUnique x (x^2 = 1).Question 16AnswerTrue False

Let the universe of discourse be the set of real numbers. By selecting True or False, give the truth value of the following:ForEvery x ForEvery y ThereExists z (x + y = z^2).Question 3AnswerTrue False

Let the universe of discourse of x and y be the set of real numbers.Let P(x) denote "x is even." Let Q(x) denote "x is an integer."Then, "Every integer is odd." can be expressed asQuestion 1Answera.ForEvery x [ NOT Q(x) OR NOT P(x) ].b.ForEvery x NOT P(x).c.None of the Given Choices.d.ForEvery x [ P(x) AND Q(x) ].e.ForEvery x [ P(x) -> Q(x) ].

Let the universe of discourse of x and y be the set of integers.Let P(x, y) denote "x = y^2."Then, from the following, the one that is False isQuestion 7Answera.ForEvery x ThereExists y NOT P(x, y).b.ForEvery y ThereExists x P(x, y).c.ThereExists x ForEvery y NOT P(x, y).d.ForEvery x ThereExists y P(x, y).

1/2

Upgrade your grade with Knowee

Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.