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9 April, 01:19

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 3 15 even? (c) The sum of 3 and 4 is 12. (d)

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  1. 9 April, 01:44
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    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 3 15 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 3 15 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
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