MATH 1190 Midterm: Math 1190 - test 2
18 Feb 2019
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The total number of points for the test is 65: (5 points) for a non-empty set x, let f : x p (x) be de ned by f (x) = {x} for all x x. Prove that f is injective and not surjective. If x1 6= x2, then {x1} 6= {x2}, that is, f (x1) 6= f (x2), so f is injective. Clearly p (x), but f 1({ }) = , so f (x) 6= p (x), that is, f is not surjective. 2. (5+5+5 points) (a) prove the equality using the properties of the oor and ceiling functions. 3(cid:5) = n z, we have n = (cid:22)(cid:18)x + 8 = 43. 75 = 44. (b) using the ceiling function determine how many bytes are required to encode. 2000: (5 points) using the sums of rst n terms of geometric progressions nd the value of the sum. Xk=0 (2 3k 3 2k).
