Question

Let f : A → B and g : B → C. For each of the...

Let f : A → B and g : B → C. For each of the statements in this problem determine if the statement is true or false. No explanation is required. Just put a T or F to the left of each statement.

a. g ◦ f : A → C

b. If g ◦ f is onto C, then g is onto C.

c. If g ◦ f is 1-1, then g is 1-1.

d. Every subset of an uncountable set is uncountable.

e. If f : X → Y and is onto Y , then Y <∼ X.

f. If f −1 and g −1 are functions, then g ◦ f has an inverse.

g. If A is uncountable, then P(A) is uncountable.

h. Every subset of a countable set is countable.

i. Every subset of a denumerable set is denumerable.

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