The next few exercises ask you to address the converse of the last few. Supposing that T ◦ R has the listed property, can you infer that both relations R and T have the same property? Only R? Only T?...

The next few exercises ask you to address the converse of the last few. Supposing that T ◦ R has the listed property, can you infer that both relations R and T have the same property? Only R? Only T? Neither? Prove your answers.

1 T ◦ R is a function. Must T be a function? R? Both?

2 T ◦ R is a one-to-one function and R and T are both functions. Must T be one-to-one? R? Both?

3 T ◦ R is an onto function and R and T are both functions. Must T be onto? R? Both?