NATURAL NUMBER {1,2,3....}
INTEGER NUMBER {...-3,-2,-1,0,1,2,3....}
The FUNCTION O:AXA→A is defined as o(a,b)=aob is called binary operation if aob∈ A
EXAMPLE : ADDITION
+:NXN → N,
+(a,b)=a+b
a,b∈ N
2+3=5
3,2 belongs to natural number and resultant 5 is also belong to natural number so addition is a binary operation
EXAMPLE : subtraction
-:NXN → N,
-(a,b)=a-b
a,b∈ N
2-=-1
2,3 belongs to natural number and resultant(-1 is not belong to natural number so subtraction is not a binary operation
EXAMPLE : multiplication
*:NXN→ N,
*(a,b)=a*b
a,b∈ N
2*3=6
2,3 belongs to natural number and resultant(6 is also belong to natural number so multiplication is a binary operation)
EXAMPLE : division
:NXN→ N,
%(a,b)=a%b
a,b∈ N
2%3=0.6
2,3 belongs to natural number and resultant(0.6 is not belong to natural number so division is not a binary operation)
EXAMPLE : exponential
^:NXN→ N,
^(a,b)=a^b
a,b∈ N
23=8
2,3 belongs to natural number and resultant(8 is also belong to natural number so exponential is also a binary operation)
EXAMPLE : exponential
^:IXI→ I,
^(a,b)=a^b
a,b∈ I
2-3=1%8=0.12
2,-3 belongs to integer number and resultant(1%8 is NOT belong to integer number so exponential is not a binary operation)
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