Answer:
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