Question

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

1. Boston is a capital of Massachusetts
2. Miami is the capital of Florida
3. $2+3=5$
   
4. $5+7=10$
   
5. $x+2=11$
   
6. Answer this question

Short answer

1. ANSWER is TRUE.
   It is a proposition.
2. ANSWER is FALSE.

It is a proposition.

1. ANSWER is TRUE.
   It is a proposition.
2. ANSWER is FALSE.

It is a proposition.

1. ANSWER can be TRUE or FALSE.

It is not a proposition.

1. ANSWER is not declarative

It is not a proposition.

Step-by-step solution

Definition of proposition

Proposition:
1. It is a declarative statement which can be either true or false.
2. It cannot be both true and false simultaneously.

Statement in a) is a proposition

Boston is a capital of Massachusetts.

Given statement is true. Hence, it is a proposition.

So the answer is TRUE.

Statement in b) is a proposition

Miami is not the capital of Florida.

Given statement is false. Hence, it is a proposition.

So the answer is FALSE.

Statement in c) is a proposition.

We write the given statement as,

$2+3=5$.

Given statement is true. Hence, it is a proposition.

So the answer is TRUE.

Statement in d) is a proposition

We write given statement as,

$5+7=10$.

Given statement is false. Hence, it is a proposition.

So the answer is FALSE.

Statement in e) is not a proposition

We write given statement as,

$x+2=11$

Given statement is neither true nor false. Hence, it is not a proposition.

So the answer is not a proposition

Statement in f) is not a proposition

We write given statement as,

Answer this question.

Given statement is not declarative. Hence, it is not a proposition.

So the answer is not a proposition.