## Discrete Mathematics and Its Applications, Seventh Edition

Published by McGraw-Hill Education

# Chapter 1 - Section 1.1 - Propositional Logic - Exercises - Page 12: 1

#### Answer

a) proposition; true b) proposition; false c) proposition; true d) proposition; false e) not a proposition f) not a proposition

#### Work Step by Step

By definition, a proposition is a declarative statement that is either true or false, exclusively, therefore: a) "Boston is the capital of Massachusetts" is a declarative statement, and Boston is the capital of Massachusetts, therefore this is a true declarative statement, and therefore a proposition. b) "Miami is the capital of Florida" is a declarative statement, and Miami is not the capital of Florida, therefore this is a false declarative statement, and therefore a proposition. c) "2 + 3 = 5" is a declarative statement, and 2 + 3 = 5 is true, therefore this is a proposition. d) "5 + 7 = 10" is a declarative statement, and 5 + 7 = 10 is false, therefore this is a proposition. e) "x + 2 = 11" is a declarative statement, however, there is no definitive truth value associated with this statement using the given information. For instance, if x = 9, then this statement is true, but if x = 3, then this statement is false. Since there is no way to determine the value of x with the given information, this is not a proposition. f) "Answer this question." is an imperative, not declaratory, statement, and is therefore not a proposition.

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