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Question

Which of the following binary operations defined on the set of real numbers is not associative?


A

Addition

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B

Subtraction

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C

Multiplication

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D

Division

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Solution

The correct options are
B

Subtraction


D

Division


A binary operation is associative if a (b c) = (a b) c. Addition and multiplication are associative because a(bc) = (ab)c = abc and a+(b+c) = (a+b)+c. But we can see that subtraction and division are not associative because a-(b-c) is not equal to (a-b)-c and a(bc) is not equal to (ab)c. So two of the given functions are not associative.


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