II. Write the negation of the statement : х, у R, х2 + у2 %3 9 Write the negation of the statement: xZ, such that x is prime or x? 4 (c) For the given statement, Write the contrapositive for the statement below: If today is Thanksgiving, then today must be Thursday (d) Give a counterexample to disprove the statement below : X, y Irrationals, the product, xgy , is irrational.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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**III.**

- Write the negation of the statement:
  \(x, y \in \mathbb{R}, \, x^2 + y^2 = 9\)

- Write the negation of the statement:
  \(x \in \mathbb{Z}\), such that \(x\) is prime or \(x^2 < 4\)

(c) For the given statement, write the contrapositive for the statement below:
   *If today is Thanksgiving, then today must be Thursday.*

(d) Give a counterexample to disprove the statement below:
   *\(x, y\) Irrationals, the product, \(x \times y\), is irrational.*
Transcribed Image Text:**III.** - Write the negation of the statement: \(x, y \in \mathbb{R}, \, x^2 + y^2 = 9\) - Write the negation of the statement: \(x \in \mathbb{Z}\), such that \(x\) is prime or \(x^2 < 4\) (c) For the given statement, write the contrapositive for the statement below: *If today is Thanksgiving, then today must be Thursday.* (d) Give a counterexample to disprove the statement below: *\(x, y\) Irrationals, the product, \(x \times y\), is irrational.*
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