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CS 336 PreTest_sets_2_solutions

# CS 336 PreTest_sets_2_solutions - CS 336 Pre-Test 2 Sets 3...

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CS 336 Pre-Test 2 Sets 3. Sets 3.1* What are these sets? Write them using braces, commas, numerals, … (for infinite sets), and only. N is the set of natural numbers. ( P ( S ) is the power set of S .) a) ({1, 3, 5} {3, 1}) {3, 5, 7} = {1, 3, 5} {3, 5, 7} = {3, 5} b) {{A}, {A, 5}, {{5, 7}, {7, 9}}} = {{A}, {A, 5}, {7}} = {A, 5, 7} c) ({1, 2, 5} - {5, 7, 9}) ({5, 7, 9} - {1, 2, 5}) = {1, 2} {7, 9} = {1, 2, 7, 9} d) {1} { } = {1, } e) P ({7, 8, 9}) – P ({7, 9}) = { , {7}, {8}, {9}, {7, 8}, {7, 9}, {8, 9}, {7, 8, 9}} – { , {7}, {9}, {7, 9}} = {{8}, {7, 8}, {8, 9}, {7, 8, 9}} f) P ( ) = { } g) { x : x is an integer and x 2 = 2 } = h) { x : 5 y N where x = y 2 } = {0, 1, 4, 9, 16, …} i) {1} × {1, 2} × {1, 2, 3} = {(1, 1, 1), (1, 1, 2), (1, 1, 3), (1, 2, 1), (1, 2, 2), (1, 2, 3)} j) × {1, 2} = k) P ({1, 2}) × {1, 2} = { , {1}, {2}, {1, 2}} × {1, 2} = {( , 1), ( , 2), ({1}, 1), ({1}, 2), ({2}, 1), ({2}, 2) ({1, 2}, 1), ({1, 2}, 2)}

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3.2* What is the cardinality of each of the following sets? Justify your answer. N is the set of natural numbers ( i.e. , the non-negative integers.) a) S = { , { }} | | 2 S = , since S contains exactly two elements: the empty set and the set whose
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CS 336 PreTest_sets_2_solutions - CS 336 Pre-Test 2 Sets 3...

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