# homework1 - p a c t Find A and B Then ﬁnd n A and n B...

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MATH 1190: HOMEWORK 1 Please attempt all of these problems, and bring your solutions to class on September 22, 2010. The solutions will be discussed in class. Some of the problems are routine, while some are a little more challenging. Q1. Find the cardinalities of the following sets: A = {- 2 , - 1 , 0 , 1 , 2 , 3 , 4 } , B = { c, a, s, a, b, l, a, n, c, a } , C = { x | x is an odd integer between 10 and 20 } , D = { 1 2 , 1 5 , 1 8 , . . . , . . . , 1 59 } , E = { x | x is an integer such that 3 x + 7 = 20 } . Q2. Determine whether the following statements are true or false. (Note that we have deﬁned the sets N , Z , Q in class.) ( a ) 11 3 N , ( b ) - 171 3 Z , ( c ) 4 . 31 Q , ( d ) { 0 , 3 , 5 } ⊆ N , ( e ) {- 1 6 , 34 , 16 } ⊂ Q . Q3. Let U = { a, b, c, e, p, q, t, x, y } be the universal set, and A = { c, a, p } , B =
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Unformatted text preview: { p, a, c, t } . Find A and B . Then ﬁnd n ( A ) and n ( B ). Which of the following statements are true? A ⊆ B, A ⊂ B, B ⊆ A , B ⊆ A , ∅ ⊂ A , B ⊂ ∅ . Q4. Let A = { p, q, r } , B = { p, q, r, s, t } . Find all sets C which satisfy both of the following properties: A ⊂ C, and C ⊂ B. There are also lots of exercises at the end of chapters 1.1 and 1.2 in the textbook. Depending on your own judgement, you should attempt as many of them as necessary. You should feel completely conﬁdent that you under-stand the concepts involved....
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