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Determinewhether or not eachof thedefinition of given below gives a binary operation. In theevent that isnot a binary operation, given justificantion for this. (i) On Z^(+), define * by a * b = a- b (ii)On Z^(+), define * by a * b = ab (iii) On R,define * by a * b - ab^(2) (iv) On Z^(+), define * by a *b = |a - b| (v)On Z^(+), define * by a* b = a |
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Answer» Solution :In `Z^(+), a ** B =a - b` `2**3 = 2-3 = -1 in Z^(+)` `THEREFORE` Given operation is notbinary. (ii) In `Z^(+), a ** b = ab` The product of every TWO positive intergers is a positiveinterger. `therefore` Given operations is binary. (iii) In R,`a ** b= ab^(2)` The square of every real NUMBERIS always a real number. (iv)In `Z^(+) , ""a**b = a` The modulus of the difference ofevery two positiveinteger. `therefore` Givenoperation in binary. (v)`In Z^(+), "" a**b=a` For each `a,b in Z^(+)` `""a * b = a in Z^(+)` `therefore` Given operation is binary. |
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