Suppose S = {1} and T = {a, b}, and recall that a function from a set S to a set T can be specified as a subset of the cross product S x T.

a. Specify as a subset of the cross product S x T an onto function from S to T, or explain why no such function exists.

(1,a), (1,b)

b. Specify as a subset of the cross product S x T a one-to-one function from S to T, or explain why no such function exists.

2. Define the sets R and S as follows:

R = {a, b, c}

S = {a, b}.

a. Give one element of S x R that are not in R x S, or explain why no such element exists.

b. Explain why R x R is or is not a subset of R x S.