Question

Question five

For each of the following sentences, write the sentence in logical notation , negate the sentence , and say whether the sentence or its negation is true.
a) Given any integer, there is a larger integer.

Answer 1

Answer provided by https://www.AssignmentExpert.com

Answer on Question #75986 – Math – Discrete Mathematics Question

Write the sentence in logical notation, negate the sentence, and say whether the sentence or its negation is true.

Given any integer, there is a larger integer

Solution

Logical notation:

$$\forall x \in Z, \exists y \in Z \text{ such that } y > x$$

Negation:

For some integers there is no a smaller integer.

$$\exists x \in Z \text{ such that } \forall y \in Z, y < x$$

Answer: the sentence is true, its negation is false.