Draw the composite table for the operation * defined by x*y=x,x, y  S  {a,b,c, d}.

To draw the composite table for the operation * defined by x*y=x, for all x, y in S = {a, b, c, d}, we need to perform the operation * on each pair of elements in S.

First, let's list all the elements in S: a, b, c, d.

Next, we will create a table with the elements of S as both the row and column headers. This will give us a square table with four rows and four columns.

Now, we will fill in the table by performing the operation * on each pair of elements. According to the definition x*y=x, we can see that the result of the operation * will always be equal to the first element in the pair.

The completed composite table for the operation * is as follows:

In this table, each cell represents the result of the operation * on the corresponding pair of elements from S. As we can see, the result is always equal to the first element in the pair, as defined by the operation *.

This is the composite table for the operation * defined by x*y=x, for all x, y in S = {a, b, c, d}.