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Answer the following brief question: (1) Given a set X the power set P(X) is ......

Answer the following brief question:

(1) Given a set X the power set P(X) is ...

(2) Let X, Y be two infinite sets. Suppose there exists an injective map f : X → Y but no surjective map X → Y . What can one say about the cardinalities card(X) and card(Y ) ?

(3) How many subsets of cardinality 7 are there in a set of cardinality 10 ?

(4) How many functions are there from X = {1, 2, 3, . . . , 20} to {1, 2, . . . , 7} ?

(5) What does it mean that a set X is countable? (6) Is the set Q of rational numbers countable? (7) Give an example of an uncountable set.

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