Quiz 2 solutions

# Quiz 2 solutions - Math 100 Quiz 2 Martin H Weissman...

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Unformatted text preview: Math 100 Quiz 2 Martin H. Weissman Instructions: Please answer the following questions clearly, concisely and neatly. Partial credit will be given on Problems 4, 5, and 6. In addition, points may be deducted for disorganized or illegible responses. All proofs should be written in complete sentences with correct English grammar and punctuation. Avoid abbreviating English words when possible. Question: 1 2 3 4 5 6 Total Points: 1 1 1 2 2 3 10 Score: 1. (1 point) Let S = { 2 , 3 , 5 , 6 } . Let P ( S ) be the set of subsets of S . Let P ( S ) 2 be the set of ordered pairs, whose entries are elements of P ( S ). How many elements does P ( S ) 2 have? Solution: Since S has 4 elements, P ( S ) has 2 4 = 16 elements. Therefore, P ( S ) 2 has 16 2 = 256 elements. 2. (1 point) How many natural numbers between 15 and 270 are multiples of 3 or multiples of 7 (or both)? Solution: Among the natural numbers between 15 and 270, the multiples of 3 are the numbers 15 , 18 , 21 ,..., 270. These are in bijection with the numbers 5 , 6 , 7 ,..., 90, which are in bijection with the numbers 1 , 2 , 3 ,..., 86. Hence, there are 86 multiples of 3 between 15 and 270....
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Quiz 2 solutions - Math 100 Quiz 2 Martin H Weissman...

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