Question

Please help!
Determine if the following statement is always true. If it isn't, provide a counterexample.

If the mathematical operation* is defined for all numbers x and y as 2x+3y, then the operation* is commutative.

WILL REWARD MEDAL!!! thank you

Answer 1

@lilai3 replace x by y and y by x
then the operation will result out 2y+3x
Is this same as 2x+3y?

Answer 2

...uhm....yes?

Answer 3

2y+3x ? 2x+3y
put x=2 and y=3
what would you get for both?

Answer 4

1. 12
2.10

Answer 5

Are the results same?

Answer 6

no!

Answer 7

btw, thanks for the medal! (;

Answer 8

Good that implies
\[2x+3y\ne 2y+3x\]
Therefore changing the order of operands changes the operation's result.
Do you follow this?

Answer 9

yes.

Answer 10

This implies that is not a commutative operation.
Suppose if we had the operation such as 2x+2y
replace x by y and y by x
we'll get
2y+2x
which is same as the original.
So changing the order of operands doesn't change the operation.
So 2x+2y is commutative.

Answer 11

@lilai3 Do you follow the counter example I gave?

Answer 12

so it isn't always true

Answer 13

yes, we have to check and then only we can conclude about the property.

Answer 14

Do you follow?

Answer 15

oh. sorry. yes. thank you!

Answer 16

Cool :P