Let A be Q/{1}. Define * on A by x * y=x+y-xy. Is * binary on A? If so, examine the commutative and association properties satisfied by * on A.

Let A be Q/{1}. Define * on A by x * y=x+y-xy. Is * binary on A? If so, examine the existence of identity & inverse properties for the operation * on A.

Let M={[{:(,x,x),(,x,x):}}: x in R-{0}} and let * be the matrix multiplication. Determine whether M is closed under *. If so, examine the commutative and associative properties satisfied by * on M.

Define an operation * on Q as follows: a * b =((a+b)/(2)), a, b in Q . Examine the closure, communative, and associative properties satisfied by * on Q.

Let S be a non-empty set and 0 be a binary operation on s defined by x 0 y =x, x, y in S . Determine whether 0 is commutative and association.

Let A ={1,2,3,…… 14 } R is a relation on A defined by R = {(x,y),3x -y=0 ,x,y in A } find the domain , and range or R .