MATH-0061 Midterm: Math 61-02 Midterm 1
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Instructions: every answer requires some justi cation that"s what the white space is for. On proof problems, if you don"t have a full proof, give a proof strategy. (1) (a) [1 min] what is the contrapositive of if you cheat on this test on monday, i will murder you on wednesday ? (b) [3 mins] prove that a b = a a b b. (d) [5 mins] name three distinct elements of p (cid:16)p(cid:16)[3] \ {1}(cid:17)(cid:17). [8 mins] consider the statement rn : n! Prove that this is true for in nitely many values n n. (2) [13 mins] suppose i have a large supply of sugarcubes and 10 people"s co ee mugs, numbered 1 10. A distribution of sugarcubes is just a way of putting some cubes in some mugs. For instance, put 6 sugarcubes in mug 3, and no cubes in any other mug is one way of distributing six cubes.
