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Consider the following statement. v integer n, if n is divisible by 6, then n is divisible by 2 and n is divisible by 3. Which of the following is a negation for the statement? Ov integer n, if n is divisible by 6, then n is not divisible by 2 or n is not divisible by 3. O 3 an integer n such that n is divisible by 6 and either n is not divisible by 2 or n is not divisible by 3. O3 an integer n such that n is not divisible by 6 and either n is not divisible by 2 or n is not divisible by 3. O 3 an integer n such that n is not divisible by 6 and n is divisible by 2 and n is divisible by 3. Ov integer n, if n is divisible by 2 and n is divisible by 3, then n is not divisible by 6.

Consider the following statement. v integer n, if n is divisible by 6, then n is divisible by 2 and n is divisible by 3. Which of the following is a negation for the statement? Ov integer n, if n is divisible by 6, then n is not divisible by 2 or n is not divisible by 3. O 3 an integer n such that n is divisible by 6 and either n is not divisible by 2 or n is not divisible by 3. O3 an integer n such that n is not divisible by 6 and either n is not divisible by 2 or n is not divisible by 3. O 3 an integer n such that n is not divisible by 6 and n is divisible by 2 and n is divisible by 3. Ov integer n, if n is divisible by 2 and n is divisible by 3, then n is not divisible by 6.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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**Consider the following statement.** ∀ integer \( n \), if \( n \) is divisible by 6, then \( n \) is divisible by 2 and \( n \) is divisible by 3. **Which of the following is a negation for the statement?** - ☐ ∀ integer \( n \), if \( n \) is divisible by 6, then \( n \) is not divisible by 2 or \( n \) is not divisible by 3. - ☐ ∃ an integer \( n \) such that \( n \) is divisible by 6 and either \( n \) is not divisible by 2 or \( n \) is not divisible by 3. - ☐ ∃ an integer \( n \) such that \( n \) is not divisible by 6 and either \( n \) is not divisible by 2 or \( n \) is not divisible by 3. - ☐ ∃ an integer \( n \) such that \( n \) is not divisible by 6 and \( n \) is divisible by 2 and \( n \) is divisible by 3. - ☐ ∀ integer \( n \), if \( n \) is divisible by 2 and \( n \) is divisible by 3, then \( n \) is not divisible by 6.
Transcribed Image Text:**Consider the following statement.** ∀ integer \( n \), if \( n \) is divisible by 6, then \( n \) is divisible by 2 and \( n \) is divisible by 3. **Which of the following is a negation for the statement?** - ☐ ∀ integer \( n \), if \( n \) is divisible by 6, then \( n \) is not divisible by 2 or \( n \) is not divisible by 3. - ☐ ∃ an integer \( n \) such that \( n \) is divisible by 6 and either \( n \) is not divisible by 2 or \( n \) is not divisible by 3. - ☐ ∃ an integer \( n \) such that \( n \) is not divisible by 6 and either \( n \) is not divisible by 2 or \( n \) is not divisible by 3. - ☐ ∃ an integer \( n \) such that \( n \) is not divisible by 6 and \( n \) is divisible by 2 and \( n \) is divisible by 3. - ☐ ∀ integer \( n \), if \( n \) is divisible by 2 and \( n \) is divisible by 3, then \( n \) is not divisible by 6.
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