Which of these sentences are propositions? What are the truth values of those that are propositions?

QUESTION

Which of these sentences are propositions? What are the truth values of those that are propositions?a) Boston is the capital of Massachusetts.b) Miami is the capital of Florida.c) 2 + 3 = 5.d) 5 + 7 = 10.e) x + 2 = 11.f ) Answer this question.

SOLUTION

Step-by-step explanation:

Proposition:

• It is a declarative statement that is either false or true.
• It cannot be both true or false.

a) Boston is the capital of Massachusetts.

The given statement is true. Hence, the given statement is a proposition.

$ANSWER = True$

b) Miami is the capital of Florida.

The given statement is false. Hence, the given statement is a proposition.

$ANSWER = False$

c) $2 + 3 = 5.$

The given statement is true. Hence, the given statement is a proposition.

$ANSWER = True$

d) $5 + 7 = 10.$

The given statement is false. Hence, the given statement is a proposition.

$ANSWER = False$

e) $x + 2 = 11.$

The given statement can neither be true or false. It depends on the value of x. Hence, it is not a proposition.

$ANSWER =$ Not a proposition

f ) Answer this question.

The given statement is not a declarative in nature. Hence, it is not a proposition.

$ANSWER =$ Not a proposition