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# review1 - EECS 203 Midterm#1 Review Multiple Choice...

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Unformatted text preview: EECS 203 Midterm #1 Review Multiple Choice Questions Discrete Math Jeopardy Propositional Predicate Sets and Logic Logic Functions 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500 Propositional Logic: 100 Of tautology, contingency, and contradiction, what (P ^ Q) v ~P is. ANSWER BACK Propositional Logic: 100 Answer What is a contingency? BACK TO QUESTION BACK TO GRID Propositional Logic: 200 If P denotes "Water freezes" and Q denotes "The temperature is below 32oF", the correct representation of "For water to freeze, it's sufficient for the temperature to be below 32oF." ANSWER BACK Propositional Logic: 200 Answer What is Q P BACK TO QUESTION BACK TO GRID Propositional Logic: 400 Given these axioms ~P v Q R v (S ^ V) False v ~U P U (Q ~Q) v ~V the axioms from the following set that are entailed: (a) R v (S ^ V) (b) S (c) True R ANSWER BACK Propositional Logic: 400 Answer What are R v (S ^ V) and (c) True R BACK TO QUESTION BACK TO GRID Propositional Logic: 500 If you are given the four cards shown below, and asked to verify the premise beneath them by turning over as few cards as possible, the cards you would turn over. A M 4 7 "If there is a vowel on one side, there is an even number on the other side" [Watson 68] ANSWER BACK Propositional Logic: 500 Answer What are A and 7 BACK TO QUESTION BACK TO GRID Predicate Logic: 100 If all the students at the U of M speak English, and all the students at the Sorbonne speak French, the sentences from the following that are true: x [speaks-French(x) [speaksSorbonneSorbonnestudent (x)] x [~UM-student(x) V speaks-English(x)] [~UMspeaksx [UM-student(x) [UM~speaks~speaks-English(x)] BACK (a) (b) (c) ANSWER Predicate Logic: 100 Answer What are x [~UM-student(x) V speaks[~UMspeaksEnglish(x)] and (c) x [UM-student(x) [UM~speaks~speaksEnglish(x)] (b) BACK TO QUESTION BACK TO GRID Predicate Logic: 200 Of the following, the sentences that are logically equivalent to ~xy [(P(x) ^ Q(y)) R(x,y)] (a) (b) (c) x y [(~P(x) ^ ~Q(y)) R(x,y)] x y [~P(x) v ~Q(y) v R(x,y)] x y [P(x) ^ Q(y) ^ ~R(x,y)] ~R(x,y)] BACK ANSWER Predicate Logic: 200 Answer What is (c) x y [P(x) ^ Q(y) ^ ~R(x,y)] ~R(x,y)] BACK TO QUESTION BACK TO GRID Predicate Logic: 300 If the domain of discourse for x, y, and z is the real numbers, the sentences below that are true: (a) (b) (c) x y [(x <y) v (y < x)] x y z [(x <y) ( (x <z) ^ (z < y) )] x y [ (x < y) v (y < x)] ANSWER BACK Predicate Logic: 300 Answer What is (b) x y z [(x <y) ( (x <z) ^ (z < y) )] BACK TO QUESTION BACK TO GRID Predicate Logic: 500 If B(x,y) denotes "student x bought ticket y", the predicate logic representation for "Every student bought exactly one ticket." ANSWER BACK Predicate Logic: 500 Answer What is x y B(x,y) ^ B(x,y) x y z (y z ~(B(x,y) ^ B(x,z)) ~(B(x,y) BACK TO QUESTION BACK TO GRID Sets and Functions: 100 The cardinality of the set { {a, b, {c}}, d, {{e}}, f, g} ANSWER BACK Sets and Functions: 100 Answer What is 5? BACK TO QUESTION BACK TO GRID Sets and Functions: 200 The cardinality of the power set of the power set of {a,b,c} ANSWER BACK Sets and Functions: 200 Answer What is 2 8 = 256 ? BACK TO QUESTION BACK TO GRID Sets and Functions: 300 If A = {1, 2, 3, 4, 5}, B = {x| x is even ^ x Z}, and C = {x| 0 < x < 2 ^ x Z}, which of the following sentences are true : (a) (b) (c) (d) |A B| < |B C| CA {2} A B ABC BACK ANSWER Sets and Functions: 300 Answer What is (b) CA BACK TO QUESTION BACK TO GRID Sets and Functions: 400 Of the functions below, the ones that are injective: (a) (b) (c) (d) f: ZZ ,where f(x) = |x| - 17 f: people dates, where f(x) = birthday (x) f: sets of integers integers, where f(x) = the smallest element of x f: Z+ R, where f(x) = y iff x degrees Celcius converts to y degrees Fahrenheit BACK ANSWER Sets and Functions: 400 Answer What are (a) f: Z- Z where f(x) = |x| - 17 (d) f: Z+ R, where f(x) = y iff x degrees Celcius converts to y degrees Fahrenheit BACK TO QUESTION BACK TO GRID Sets and Functions: 500 If f is a function from A to B, S A, and T A, the sentences from amongst the following that are necessarily true: (a) (b) (c) (d) f(S U T) = f(S) U f(T) f(S T) = f(S) f(T) |f(S U T)| = |f(S)| + |f(T)| |f(S T)| = |f(S)| - |f(T)| ANSWER BACK Sets and Functions: 500 Answer What are (a) f(S U T) = f(S) U f(T) BACK TO QUESTION BACK TO GRID ...
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