a1 - Department of Mathematics and Statistics McGill...

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Department of Mathematics and Statistics McGill University MATH 242 Assignment 1 Due in class, Monday September 21 Full credit can be obtained from correct answers to questions totalling 70 points. 1. (10 points) Let f : X Y , A X and B Y , then prove or disprove by counterexample the statement f ( A f - 1 ( B )) = f ( A ) B . 2. (10 points) Let f : X Y , A X and B Y , then prove or disprove by counterexample the statement f ( A f - 1 ( B )) = f ( A ) B . 3. (10 points) Let f : X Y , g : Y Z and T X . Then prove or disprove by counterexample the statement ( g f )( T ) = g ( f ( T )) . 4. (10 points) Let f : X Y and g : Y Z be surjections. Then prove or disprove by counterexample the statement that g f is a surjection. 5. (10 points) Show that n X k =2 k ( k + 3) = 1 3 ( n - 1)( n + 3)( n + 4) for n N . 6. (10 points) Show that n X k =1 1 k ( k + 2) = n (3 n + 5) 4( n + 1)( n + 2) . 7. (10 points)
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a1 - Department of Mathematics and Statistics McGill...

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