m325kprac3 - n , 8 | 3 2 n-1. 6. Prove that 3 7 is...

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M325K Sample Test 3 4.6–6.3 1. Let U = { 1 , 2 , 3 ,..., 10 } be the universal set and let A = { 2 , 4 , 6 } and B = { 1 , 4 , 5 } . Find the number of elements in A c B c , A c Δ B c , and P ( A × B ). 2. Use induction to prove that the sum of the first n odd positive integers equals n 2 . 3. Prove that 2 n + 1 < n 3 for all integers n 2. 4. Prove that if A B , then A B = B . 5. Use mathematical induction to prove that for all positive integers
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Unformatted text preview: n , 8 | 3 2 n-1. 6. Prove that 3 7 is irrational. 7. Prove there are innitely many primes of the form 6 k + 5 where k is an integer. 8. If A,B, and C are sets, prove that A ( B C ) = ( A B ) ( A C ) . 9. Let A and B be sets. Construct an algebraic proof that A-( A B ) = ( A-B ) ....
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