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Midterm_Practice_sol - Midterm Practice Problems 1 Define...

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Midterm Practice Problems 1. Define the operation * on the set of all integers by: * ( x y 5 x y = + ) . A. Is the operation * associative? B. Is the operation * commutative? C. Does there exist an identity element? D. If there is an identity element, which integers have inverses?
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2. Define the function by : f Z Z x even ( ) x odd x 1 f x 2x = Find A. , when S={-2, 0, 2, 3, 5} ( ), ( ( )) 1 f S f f S B. when T = {-2, -1, 0, 1, 2} ( ), ( ( )) 1 1 f T f f T C. Does f have a left inverse? D. Does f have a right inverse?
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3. The following relation R is defined on the set Z of all integers. xRy if and only if 3x is a multiple of 7. 10y + Prove or disprove that R is an equivalence relation.
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