303a2solns - ASSIGNMENT 2 SOLUTIONS MATH 303, FALL 2011 If...

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Unformatted text preview: ASSIGNMENT 2 SOLUTIONS MATH 303, FALL 2011 If you find any errors please let me know. Manipulation (M1) ( A B ) = ( { b, d, q } { b, d } ) = ( { b, d, q } ) = { a } = A (M2) A- B = { 1 , { 3 , 8 } , 4 } - { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 } = {{ 3 , 8 }} (M3) Yes it is an ordered pair. Let us unravel this set. It has two elements, one of which is a singleton containing {{}} , and so the first coordinate of the pair is {{}} . The other element is a set with two elements, one of which is {{}} and the other is {} , thus the second coordinate is {} , and the whole thing is an ordered pair. (M4) No this set is not an ordered pair. It has a single element, so if it were an ordered pair it would be an ordered pair ( c, c ) for some c . Thus this set would be {{ c }} . However the single element of the given set is not a singleton, and so it is not an ordered pair. (M5) Lets work from the inside out: A B = { a, b } P ( A B ) = , { a } , { b } , { a, b } P ( P ( A B )) = , , { a } , { b } , { a, b } , , { a } , , { b } , , { a, b } , { a } , { b } , { a } , { a, b } , { b } , { a, b } , , { a } , { b } , , { a } , { a, b } , , { b } , { a, b } , { a } , { b } , { a, b } , , { a } , { b } , { a, b } The elements in boxes are the ones in A B ....
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303a2solns - ASSIGNMENT 2 SOLUTIONS MATH 303, FALL 2011 If...

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