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MARC GABRIEL HIZOLE

Reminder: SOLUTIONS AND/OR EXPLANATIONS TO YOUR ANSWERS ARE REQUIRED. FOLLOW INSTRUCTIONS DURING EXAM Q1 Let the universal set U be the set of natural numbers (or the set of positive integers). And we define sets A and B as follows: A= { 2, 4, 6, 8, 10, .. .} = {the set of positive even intergers} B= { 10, 20, 30, 40, 50, . .. } Find the following sets: a: the complement set of A (that is, A') 3pts b: the intersection of sets A and B 3pts c: the cardinality of the union of sets A, B; 4pts [hint: use the formula for n(A U B) ] Q2 Given the following sets: N= { 2, 3, 4, 5 } and L= { a, b, c } Let relation R from N to L be defined as follows: R= { (2, a), (3, a), (3, b), (4, c) } and relation S from L to N be defined as follows: S= { (a, 2), (b, 3), (b, 4), (c, 4 ) } a: Find the composition (R o S) ; 6pts b: What type of a relation is formed by (R o S)? 4pts Q3 a: Given the sets A= { a, b, c, d } and B= { 1, 2, 3, 4, 5 } Determine whether the function f from A to B (f: A -->B) with f(a)= 4, f(b)= 5, f(c)= 1, f(d)= 3 is one-to-one, onto, both or neither ? 5pts b: Let h be the function from { 1, 2, 3 } to { a, b, c } such that h(2)= a, h(3)= b, and h(1)= c. Is h invertible? And if it is, what is its inverse? 5pts [total 30 points] Irene fadriquela