indictate which of the following are propositions. For the ones which are propositions, determine the truth value.(a) The integer 24 is prime.(b) Is the integer 315 even?(c) The sum of 3 and 4 is 12.(d)

Step-by-step explanation:

When we propose an hypothesis, it is either true or false. The same goes for a proposition.

The required objective here is to determine the truth value in the following proposition.

(a) The integer 24 is prime.

(b) Is the integer 315 even?

(c) The sum of 3 and 4 is 12.

(d) -4 ∈ Ζ

From the first option:

(a) The integer 24 is prime.

The sentence is a proposition but the truth value is FALSE because a prime number is a number that can only be divide by 1 and itself but in the case of 24, Its factors include  1,2,3,4,6,8,12 and 24 which make 24 to falsify the proposition of being  a prime number.

(b) Is the integer 315 even?

This option is not a proposition but rather a question since it has a question mark, however, 315 is an odd number since it is not divisible by 2.

( c)  The sum of 3 and 4 is 12.

This is a proposition and the truth value is FALSE

The sum of 3+4 = 7  ; Hence; 7 ≠ 12

(d)   -4 ∈ Ζ

This is a proposition and the truth value is TRUE.

-4 ∈ Ζ  is read as ( minus four is an integer  (∈)  of Z )

Yes, this is a proposition and its Truth value is TRUE , since  minus four is an integer  (∈)  of Z