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Practice Quiz 1 (no solutions)

# Practice Quiz 1 (no solutions) - 4(2 points Let A = 3 4 5 6...

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Math 100 Practice Quiz 1 Martin H. Weissman On Wednesday, October 17, there will be a one-hour quiz in class. The quiz will be very similar, in format and difficulty, to the series of questions given below. 1. (1 point) Is the following sentence true or false? x R , z Z , such that z x and x z + 1 . 2. (1 point) Is the following sentence true or false? x Z , such that y Z , ( y + x )( y - x ) = y 2 - 3 . 3. (2 points) Prove that if x is not a multiple of 3, then x + 1 is a multiple of 3 or x - 1 is a multiple of 3.
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Unformatted text preview: 4. (2 points) Let A = { 3 , 4 , 5 , 6 , 7 , 8 } . Let B = { 1 , 3 , 5 , 7 , 9 } . Let C = { 2 , 4 , 6 , 8 } . Describe the following three sets: (a) ( A ∪ C ) ∩ B . (b) A ∪ ( C ∩ B ). 5. (2 points) Prove that if x is a rational number, and y is a rational number, then x · y is a rational number. 6. (2 points) Use the intermediate value theorem to prove that there exists a real number y which satisﬁes y 3 + y + 1 = 2....
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