Thread: [SOLVED] logic question

I need proving whether the following statement is true or false;

Both Alice's number and Brian's number divide Colin's number then the product of Alice's number and Brian's number must divide Colin's number.

Any help would be appreciated

Originally Posted by agingmathstudent

I need proving whether the following statement is true or false;

Both Alice's number and Brian's number divide Colin's number then the product of Alice's number and Brian's number must divide Colin's number.

Any help would be appreciated

it's not hard to think of a counter example.

let A be Alice's number, B be Brian's number, and C be Colin's number

what can you say about A = 6, B = 2 and C = 6

or A = 6, B = 3, C = 6

or A = 12, B = 24, and C = 24

or ....

Originally Posted by Jhevon

it's not hard to think of a counter example.

let A be Alice's number, B be Brian's number, and C be Colin's number

what can you say about A = 6, B = 2 and C = 6

or A = 6, B = 3, C = 6

or A = 12, B = 24, and C = 24

or ....

Am I not to presume that the numbers picked for A and B need to be divisible by C

therefore A/C and B/C then A x B/C would always be true

Originally Posted by agingmathstudent

Am I not to presume that the numbers picked for A and B need to be divisible by C

therefore A/C and B/C then A x B/C would always be true

re-read the problem. we need Alice's and Brian's number to divide Collin's number. so we want C/A and C/B to be integers

the problem is asking, if those are integers, is it true that C/(A*B) is an integer? if yes, the implication follows, if not, it doesn't