Question

Show that the binary operation on N defined by a+b=b is associative but not
commutative.
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Answer 1

Check commutative

Operation is commutative if

aob=boa

Now, aob =b and boa =1+b

So, aob # boa

Hence, operation is not commutative.

Check associative

Operation is associative if

ao(boc)= (aob) oc

(c) +b= (b) +c

bc=bc

hence it is associative