Answer to Question #248008 in Discrete Mathematics for awais

Question

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

Answer 1

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