**Problem 5:**The following statement is false; write the negation and disprove it using a counterexample:∀ x ∈ ℝ, if x < 2 then x² < 4**Explanation:**This statement claims that for all real numbers x, if x is less than 2, then the square of x is less than 4. To disprove it, we must find a counterexample where a real number x is less than 2, but x² is not less than 4.**Negation:**The negation of the statement is:There exists some x ∈ ℝ such that x < 2 and x² ≥ 4.**Counterexample:**Consider x = -3. While it is true that -3 < 2, we find that (-3)² = 9, which is greater than 4. Thus, this serves as a counterexample to the original statement.

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Description: **Problem 5:**The following statement is false; write the negation and disprove it using a counterexample:∀ x ∈ ℝ, if x < 2 then x² < 4**Explanation:**This statement claims that for all real numbers x, if x is less than 2, then the square of x is le

First we have to write negation of following statement:

Answered: 5. The following statement is false,…

Math

Advanced Math

5. The following statement is false, write the negation and disprove it using a counter example: VxeR, if x< 2 then x² <

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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