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.
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@lilai3 replace x by y and y by x
then the operation will result out 2y+3x
Is this same as 2x+3y?
2y+3x ? 2x+3y
put x=2 and y=3
what would you get for both?
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Are the results same?
btw, thanks for the medal! (;
Good that implies
Therefore changing the order of operands changes the operation's result.
Do you follow this?
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
which is same as the original.
So changing the order of operands doesn't change the operation.
So 2x+2y is commutative.
@lilai3 Do you follow the counter example I gave?
so it isn't always true
yes, we have to check and then only we can conclude about the property.