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.
