For any two integers x and y, which of the following suggests that operation of addition is commutative ?
x + y = y + x
x + y > x
x – y = y – x
x × y = y × x
Meaning of “commutative”: The result does not change when we swap the order of the numbers.
For addition, this means:
( x + y )
has the same value as
( y + x )
Example with numbers:
( 3 + 5 = 8 )
( 5 + 3 = 8 )
Both give ( 8 ), so the order didn’t matter.
Therefore, the statement that shows addition is commutative is:
( x + y = y + x )
Why the other options are not correct:
B: ( x + y > x ) — This only says the sum is bigger than one addend. It does not talk about swapping order.
C: ( x - y = y - x ) — Usually false (e.g., ( 7 - 2 = 5 ) but ( 2 - 7 = -5 )). Subtraction is not commutative.
D: ( x imes y = y imes x ) — This is about multiplication, not addition. The question asks about addition.