Examine whether the binary operation * defined on `R` by `a*b=a b+1` is associative or not.

Examine whether the binary operation* defined on R by a*b=ab+1 is associative or not.

Examine whether the binary operation ** defined on R by a**b=a b+1 is commutative or not.

Determine whether the binary operation ** on R defined by a ** b = |a -b| is commutative. Also, find the value of (-3) ** 2.

Examine whether the operation '**' defined on R by a**b=ab+1 is : (i) a binary or not (ii) if a binary operation, is it associative or not?

Show that the binary operation * defined on R by a ** b = (a + b)/2 is not associative by giving a counter example.

Determine whether the binary operation * on R defined by aast b =|a-b| is commutative. Also, find the value of (-3)^(ast) 2 .

Define binary operation on a set. Verify whether the operation * defined on Z, by a ** b = ab + 1 is binary or not.

Let '*' be the binary operation defined on R by a*b = 1 + ab AA a,binR associative butnot commutative.

Show that the binary operation ** defined on RR by a**b=ab+2 is commutative but not associative.

Prove that for binary operation defined on R such that ab=a+ 4b^(2) is not associative