Let p(x, y) represent the statement, "Person z has birthday y," where z is among all MACM 101 students and y is among al

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Let P X Y Represent The Statement Person Z Has Birthday Y Where Z Is Among All Macm 101 Students And Y Is Among Al 1 (40.9 KiB) Viewed 39 times

Let p(x, y) represent the statement, "Person z has birthday y," where z is among all MACM 101 students and y is among all calendar dates. Remember that there are 120 students in MACM and there are 365 calendar dates. (a) [3 marks] Write a plain-English version of the following statements: 3r p(x, July 11) Vr y p(x, y) Jy Vr p(x, y) (b) [3 marks] Using logic and quantifiers, write the equivalent of the plain-English sentence, "Every MACM student has a different birthday." (c) [5 marks] Prove or disprove: Vy 3x p(x, y) 2. [4 marks] Two Quick Questions Say you were tasked with proving: For all sets A, B, C, if (An B) UC = An (BUC) then CCA. (a) [2 marks] When you assume CA, and, after some sequence of steps, you conclude that (An B) UC # An (BUC), what is this an example of? (b) [2 marks] When you find specific examples of A, B, C such that C A, and (ANB)UC = An (BUC), what is this an example of?