For Problems 4 – 8, let S be an uncountable set. Label each of the following statements as true or false, and justify your answer. There exists a bijective function f : J → S.

. For nonempty sets A, B and C, let f : A → B and g: B → C be functions. (a) Prove: If g of is one-to-one, then f is one-to-one. using each of the following proof techniques: direct proof, proof by contrapositive, proof by contradiction. (b) Disprove: If go f is one-to-one, then g is one-to-one.

Let f be a function from R to R. Without using words of negation, write the meaning of “f is not an increasing function”.

For each of the following sets, say whether or not they are linearly independent. Justify your answer for each. A. B. С. 2 4 1 2 { [² 7 1 3 6 9 4 -2 3 0 0 0 3 1 6 1 -1 4 -5 0 A}