lilai3
  • lilai3
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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ash2326
  • ash2326
@lilai3 replace x by y and y by x then the operation will result out 2y+3x Is this same as 2x+3y?
lilai3
  • lilai3
...uhm....yes?
ash2326
  • ash2326
2y+3x ? 2x+3y put x=2 and y=3 what would you get for both?

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lilai3
  • lilai3
1. 12 2.10
ash2326
  • ash2326
Are the results same?
lilai3
  • lilai3
no!
lilai3
  • lilai3
btw, thanks for the medal! (;
ash2326
  • ash2326
Good that implies \[2x+3y\ne 2y+3x\] Therefore changing the order of operands changes the operation's result. Do you follow this?
lilai3
  • lilai3
yes.
ash2326
  • ash2326
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.
ash2326
  • ash2326
@lilai3 Do you follow the counter example I gave?
lilai3
  • lilai3
so it isn't always true
ash2326
  • ash2326
yes, we have to check and then only we can conclude about the property.
ash2326
  • ash2326
Do you follow?
lilai3
  • lilai3
oh. sorry. yes. thank you!
ash2326
  • ash2326
Cool :P

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