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Department
Mathematics
Course
MAT102H5
Professor
Shay Fuchs
Semester
Fall

Description
1. Let A = f▯4;▯3;▯2;▯1;1;2;3;4g . Find the following sets. No explanation is required! Note : Your answers should be explicit sets (do not use symbols such as \, [ and ▯). You may use the interval notation, and the symbol ▯ . (3 marks) (a) A \ N = f1;2;3;4g (b) A ▯ [▯10;3) = f3;4g (c) A \ Q = A = f▯4;▯3;▯2;▯1;1;2;3;4g (d) A [ (▯4;4) = [▯4;4] (e) A ▯ R = ▯ = f g 2. Find a quadratic equation with two distinct real solutions, given that the sum of the solutions is 47 and their product ▯59 . Show your work. (2 marks) Note: You can use a result from Problem Set B, but make sure you quote it properly. Solution: If r and s are two distinct solutions of the equation ax + bx + c = 0 , then we have r + s = ▯b and r▯s = c a a (this is a result from Problem Set B). b c In our case, r+s = 47 and r▯s = ▯59 , which means that ▯ = 47 and = ▯59 , and we can a a choose a=1 , b = ▯47 and c = ▯59 . The equation x ▯47x▯59 = 0 will indeed have two real solutions (as b ▯4ac=(▯47) +4▯59 > 0 ) satisfying the required solutions. 2 3. Let S = f2;3g ▯ f▯2;▯1;0g .
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