If n is a factor of 4 and n is a factor of 6, then n is a factor of 24

Propositions:
p: n is a factor of 4
q: n is a factor of 4
r: n is a factor of 6

Why is th truth set for this the set of integers

Question

If n is a factor of 4 and n is a factor of 6, then n is a factor of 24

Propositions:
p: n is a factor of 4
q: n is a factor of 4
r: n is a factor of 6

Why is th truth set for this the set of integers

rational · Answer

Does the integer 983 satisfies the given statement ?

javk · Answer

No…

rational · Answer

why not ?

rational · Answer

`If n is a factor of 4 and n is a factor of 6, then n is a factor of 24`

the implication evaluates to "true" if the premise is false

rational · Answer

F -> T is true
F -> F is also true

rational · Answer

right ?

javk · Answer

Oooh, makes sense, i get it thanks

rational · Answer

np :)

rational · Answer

the given statement evaluates to "true" no matter what integer "n" you choose
so the truth set is all integers

rational · Answer

because, if something is a factor of both 4 and 6, then it will also be a factor of 24.

rational · Answer

$d\mid 4$ and $d\mid 6$  $\implies$  $d\mid 4*6$