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On the set $N$ of non-negative integers, the binary operation ______ is associative and non-commutative.
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Define Binary operation $\ast$ on $(a,b)$ as : $a\ast b = a$

  1. It is associative : $(a\ast b)\ast c = a\ast c = a$, and $a\ast(b\ast c) = a\ast b = a$
  2. t is not commutative : $a\ast b = a$, whereas $b\ast a = b$.
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The most important associative operation that's not commutative is function composition.

If you have two functions f and g, their composition, usually denoted f∘g, is defined by 

                (f∘g)(x)=f(g(x)).
It is associative, (f∘g)∘h=f∘(g∘h),

but it's usually not commutative. f∘g is usually not equal to g∘f. 

For our case suppose $\forall$x $\in$ N of non-negative integers, if f(x)=x2 and g(x)=x+1, then (f∘g)(x)=(x+1)2 while  (g∘f)(x)=x2+1, and they're different functions.

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@Arjun sir    @Lakshman Patel RJIT

 

‘<’(smaller than)  is possible.

it is associative.

e.ge.

1<(2<3) = (1<2)<3

it is not commutative.

e.g. 

1<2 != 2<1

 

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