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Quiz1Spring07 - ∅ ∈ A × A Note that by definition A...

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Math 213, Section B1, Quiz 1 (Solutions); Friday, Jan 26, 2007 1. Let A = { , {} , 1 , 2 , { }} , B = { 1 , 2 , 3 } and C = { 1 , } . (1) Find | A | , | B | and | C | . (2) Find the sets A - B and A C . (3) Is it true that C A ? (4) Is it true that A × A ? (5) Is it true that ( A Z ) × ( A Z ) B × B ? Solution. (1) | A | = 4, | B | = 3 and | C | = 2. Note that = {} and that is why | A | = 5. (2) A - B = { , { }} and A C = { 1 , } . (3) Yes, it is true that C A . (4) No, it is not true that
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Unformatted text preview: ∅ ∈ A × A . Note that by definition A × A consists of all the ordered pairs ( a, b ) where a, b ∈ A . Thus ( ∅ , ∅ ) ∈ A × A but ∅ 6∈ A × A . (5) Yes, it is true that ( A ∩ Z ) × ( A ∩ Z ) ⊆ B × B . Note that ( A ∩ Z ) = { 1 , 2 } ⊆ B . 1...
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