Weight trаining etiquette includes returning equipment аnd wiping оff the equipment with а tоwel after use.
Yоu need tо dоwnloаd the Exаm templаte and use that to take this midterm. You also need to submit all the 8 pages in the template, even if you do not write on all of them. 1. In a village with 700 people, should there be at least two people with the same initials, where the initials of a person's name are formed by the first letter of the first name followed by the first letter of the last name? Give reasons for your answer. (20 points) 2. Prove that a function f: S -->T is 1-1, if and only if for each subset A of S, f^{-1}(f(A) )=A. (30 points) 3. For the function f(x) = (x+1)/x, (a) determine the domain and the range, with the domain as large as possible. (10 points) (b) Is f 1-1? Justify your answer. (10 points) (b) If the answer to (b) is yes, find a formula for the inverse of f. (10 points) 4. Given subsets A, B and C of a big set U, suppose A C is a subset of B C and AC is a subset of B C. Then prove that A is a subset of B. (20 points)