Q 1800191018.     Determine whether or not each of the definition of * given below gives a binary operation. In the event that * is not a binary operation, give justification for this.

(i) On `Z^(+)`, defined * by a * b `=a - b`

(ii) On `Z^(+)`, defined * by a* b `= ab`

(iii) On `R`, defined * by a * b `= ab^2`

(iv) On `Z^(+)`, defined a* b `= | a- b |`

(v) On `Z^(+)`, defined * by a* b `=a`


NCERT Chapter Solution 1.4/01

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