Underline the domain, write it symbolically and then write the negation of the following If an integer n is divisible by 6, then 2|n and 3|n. Symbolically: Negation: Which is true: the original, the negation, or neither?

Underline the domain, write it symbolically and then write the negation of the following If an integer n is divisible by 6, then 2|n and 3|n. Symbolically: Negation: Which is true: the original, the negation, or neither?

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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Question

Discrete Math

Underline the domain, write it symbolically and then write the negation of the following
If an integer n is divisible by 6, then 2|n and 3|n.
Symbolically:
Negation:
Which is true: the original, the negation, or neither?

Expert Solution

Step 1

Sol:-

Symbolically: Let D be the domain of integers. Then, the conditional statement can be represented as:

For all n ∈ D, if n is divisible by 6, then 2 | n and 3 | n.

The domain is the set of integers, denoted by D.

Negation: The negation of the conditional statement "if p, then q" is "p and not q". Applying this to the original statement, the negation would be:

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