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Unformatted text preview: Midterm solutions for MATH109 Spring Quarter 2007, UCSD Henning Hohnhold (1) Multiple Choice Questions. (10 points) In this problem, please mark all true statements. Ten correct answers are worth 10 points, nine 9 points, eight 7 points, seven 5 points, six 3 points, five 2 points, four 1 point. Three or less correct answers will not earn credit. If P ( n ), n ∈ N , is a sequence of statements, then all P ( n )’s are true if and only if for all n ∈ N we have the implication P ( n ) ⇒ P ( n + 1). Two sets S and T are equal exactly if S is a subset of T and T is a subset of S . ‘( P or Q ) ⇒ R ’ is true if and only if ‘( ¬ P and ¬ Q ) ⇒ ¬ R ’ is true. The implication ‘( P 1 ,P 2 ,P 3 , and P 4 ) ⇒ Q ’ is true if and only if ‘ ¬ Q implies that there exists an i ∈ { 1 , 2 , 3 , 4 } such that P i is false’. The function f : [0 , π 2 ] → [ 1 , 1], f ( x ) := 1 2 cos( x ), admits an inverse function g : [ 1 , 1] → [0 , π 2 ]. If the composition g ◦ f : S → U of two functions f : S → T and g : T → U is injective, then f is injective. If the composition g ◦ f : S → U of two functions f : S → T and g : T → U is surjective, then f is surjective....
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This note was uploaded on 04/30/2008 for the course MATH 109 taught by Professor Knutson during the Spring '06 term at UCSD.
 Spring '06
 Knutson
 Math

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