4023f10ps1a

# 4023f10ps1a - Homework #1 Solutions Due: August 30 2010 1....

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Homework #1 Solutions Due: August 30 2010 1. Let A = f a; b; c; d; e g , B = f 1 ; a; b; 2 ; c g , and C = f 3 ; c; a; 1 ; f g . Answer the following questions concerning these sets. Remember that the cardinality of a set S , denoted j S j , means the number of elements in the set. Also the relative diﬁerence of sets S and T , denoted S n T , is S n T = f x 2 S : s = 2 T g : That is, S n T consists of all of the element of S that are not elements of T . (a) Write the set A \ B . I Solution. A \ B = f a; b; c g J (b) Write the set A [ B . I Solution. A [ B = f a; b; c; d; e; 1 ; 2 g . J (c) Write the set A n ( B \ C ). I Solution. B \ C = f 1 ; a; c g so A n ( B \ C ) = f b; d; e g . J (d) Write the set ( A \ C ) £ ( C n B ). I Solution. A \ C = f a; c g and C n B = f 3 ; f g so ( A \ C ) £ ( C n B ) = f ( a; 3) ; ( a; f ) ; ( c; 3) ; ( c; f ) g : J (e) What is the cardinality of P ( A )? Remember that P ( A ) denotes the power set of A . I Solution. j A j = 5 so jPj = 2 5 = 32. J (f) What is the cardinality of A £ C ? I Solution. j A £ C j = j A j ¢ j C j = 5 £ 5 = 25 : J (g) Which set has more elements: P ( A £ C ) or P ( A ) £ P ( C )?

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4023f10ps1a - Homework #1 Solutions Due: August 30 2010 1....

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