7. For each operation * given below, determine whether * is a binary operation, commutative or associative. In the event that * is not a binary operation, give justification for this.
i. On Z, a*b=a-b
ii. On Q, a*b=ab+1
iii. On Q, a*b=ab/2
iv. On Z+ , a*b= 2ab
binary operation is a rule for combining two elements (called operands) to produce another element
Property of Binary Operation is closure:
if
operation is commutative if
operation is associative if
i.
binary operation
not commutative:
not associative:
ii.
binary operation
commutative:
associative:
iii.
binary operation
commutative:
associative:
iv.
binary operation
commutative:
associative:
Comments