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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