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.

In (S, **) , is defined by x ** y =x where x, y in S , then

The binary operation ** defined on a set s is said to be commutative if

A binary operation on a set S is a function from

A Relation R is given by the set {(x,y)| y= x+ 3,x in {0,1,2,3,4,5}}. Determine its domain and range .

A Relation R is given by the set {(x, y)|y=x+3, xin{0, 1, 2, 4, 5}} . Determine its domain and range.

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 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.

Let A and B be two non empty subsets of a set X such that A is not a subset of B then