Associativity of binary operations

Discuss the commutativity and associativity of binary operation* defined on Q by the rule a*b=a-b+ab for all a,b in Q

Distributivity of binary operations

Define a commutative binary operation on a set.

The number of commutative binary operations that can be defined on a set of 2 elements is (a) 8 (b) 6 (c) 4 (d) 2

Show that +" ":" "R" "xx" "R ->R and xx" ":" "R" "xx" "R ->R are commutative binary operations, but " ":" "RxxR ->R and -:" ":" "R_* xxR_* ->R_* are not commutative.

Discuss the commutativity and associativity of the binary operation * on R defined by a*b=(ab)/(4) for all a,b in R

Discuss the commutativity and associativity of the binary operation * on R defined by a*b=a-b+ab for all a,b in R, where on RHS we have usual addition,subtraction and multiplication of real numbers.

Number of binary operations

State whether the following statements are true or false.Justify.(i) For an arbitrary binary operation on a set N,a*a=a a a N( ii) If . is a commutative binary operation on N, then a*(b*c)=(c*b)*a