Need the solution for number five, please explain process of finding the solution 1. Apply a truth table to show each conclusion of following:(a) ~(-p) = p(b) ~(pVq) = (~p) ^ (~q)2. Write down the converse, inverse and contra-positive of each of the following statements:(a) For any real number x, if x >4, then x² > 16.(b) If both a and b are integers, then their product ab is an integer.3. Use logical equivalences to simplify each one of followinga) ((PA¬Q) V (PAQ)) ^Q (b)-((-p^q) v (p^-q)) v (p^q)4. Negating the following statements:(a) V primes p, p is odd.(b) 3 a triangle T such that the sum of the angles equals 200°.(c) For every square x there is a triangle y such that x and y have different colors.(d) There exists a triangle y such that for every square x, x and y have different colors.(e) V people p, if p is blond then p has blue eyes.5. Construct a truth table to determine whether or not the argument is valid(a)(b)pv (q vr)יזרpv qp→qv (¬r)q→ p^r:p →r6. Prove that(a) 9n² + 3n-2 is even for any integer n.(b) For all integers mann, m+nand m-nare either both odd or both even.(c) There are real numbers such that √a + b = √a + √b.(d) For all integers, if n is odd then n²is odd.7. Show that the following statements are false:(a) There is an integer n such that 2n² - 5n + 2 is a prime.(b) If m and n are any two positive integers then mn > m + n.

Answered: 5. Construct a truth table to determine…

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5. Construct a truth table to determine whether or not the argument is valid (a) pv (q vr) זר pv q

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter2: Equations And Inequalities

Section2.6: Inequalities

Problem 80E

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Question

Need the solution for number five, please explain process of finding the solution

1. Apply a truth table to show each conclusion of following:
(a) ~(-p) = p
(b) ~(pVq) = (~p) ^ (~q)
2. Write down the converse, inverse and contra-positive of each of the following statements:
(a) For any real number x, if x >4, then x² > 16.
(b) If both a and b are integers, then their product ab is an integer.
3. Use logical equivalences to simplify each one of following
a) ((PA¬Q) V (PAQ)) ^Q (b)-((-p^q) v (p^-q)) v (p^q)
4. Negating the following statements:
(a) V primes p, p is odd.
(b) 3 a triangle T such that the sum of the angles equals 200°.
(c) For every square x there is a triangle y such that x and y have different colors.
(d) There exists a triangle y such that for every square x, x and y have different colors.
(e) V people p, if p is blond then p has blue eyes.
5. Construct a truth table to determine whether or not the argument is valid
(a)
(b)
pv (q vr)
יזר
pv q
p→qv (¬r)
q→ p^r
:p →r
6. Prove that
(a) 9n² + 3n-2 is even for any integer n.
(b) For all integers mann, m+nand m-nare either both odd or both even.
(c) There are real numbers such that √a + b = √a + √b.
(d) For all integers, if n is odd then n²is odd.
7. Show that the following statements are false:
(a) There is an integer n such that 2n² - 5n + 2 is a prime.
(b) If m and n are any two positive integers then mn > m + n.

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