I need help with geometry..?

Question

don't understand this.. im so stupid :( just 2 questions tho ok...

tell whether the statement is true or false, state the converse of the statement, and tell whether the converse is true or false. if either is false, give a counterexample.

6. If a positive integer is divisible by both 2 and 3, then it is divisible by 12.

8. For an integer n, if n^2 is divisible by 4, then n is divisible by 4.

i just need these 2 problems and im done with my homework...

PLEASE HELP ME !!!!!! MY TEACHER DOESN'T TEACH US ANYTHING! D:

& thank you very much :D

Answer 1

6 is false.for example 18 is divisable by 3 and 2 but not by 12.... i dont know about 8!

Answer 2

6.  False. If a positive integer is divisible by both 2 and 3 it is divisible by 6.  In some instances it will also be divisible by 12, but for instance 18 is divisible by 2 and 3 but not 12

8.  False.  if n = 6 then n^2 = 36.  This is divisible by 4 but six is not.

Answer 3

THINK FOR YOURSELF!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!...

Answer 4

For six, any number is divisible by 12, the question is whether or not 12 will divide evenly.

For 6, no, any time it's 2 x 3 x (an odd number) it won't be divisible by 12, starting with 2 x 3 x 1.

For 8, no.  6 x 6 =36.  36/4= 9.  6 is not divisible (evenly) by 4.

Answer 5

For 12, if the number is divisible by 3 and 4, then it is divisible by 12. Because 12 is divisible by both 3 and 4. Therefore, the statement is TRUE.

By the definition of "divisible by 4", this means that there is some integer k so that n = 4k.

This means that n = 4k = 2(2k).

Therefore, n is divisible by four. As the previous question, this statement is also TRUE.