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(c) Give the contrapositive, the converse and the inverse of each of the following statement: i. Vx E R, if x > 3 then x2 > 9 ii. Vx E R, if x (x + 1) > 0 then x > 0 or x < –1

(c) Give the contrapositive, the converse and the inverse of each of the following statement: i. Vx E R, if x > 3 then x2 > 9 ii. Vx E R, if x (x + 1) > 0 then x > 0 or x < –1

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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(c) Give the contrapositive, the converse and the inverse of each of the following statement: i. Vx E R, if x > 3 then x2 > 9 ii. Vx E R, if x(x +1) > 0 then x > 0 or x < -1 (d) A tautology is a proposition that is always true. Let p, q and r be three propositions, show that (p → (q V r) → ((p ^ ¬q) → r) is a tautology.
Transcribed Image Text:(c) Give the contrapositive, the converse and the inverse of each of the following statement: i. Vx E R, if x > 3 then x2 > 9 ii. Vx E R, if x(x +1) > 0 then x > 0 or x < -1 (d) A tautology is a proposition that is always true. Let p, q and r be three propositions, show that (p → (q V r) → ((p ^ ¬q) → r) is a tautology.
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