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 [speaksFrench(x) [speaksSorbonneSorbonnestudent (x)] x [~UMstudent(x) V speaksEnglish(x)] [~UMspeaksx [UMstudent(x) [UM~speaks~speaksEnglish(x)]
BACK (a) (b) (c) ANSWER Predicate Logic: 100 Answer
What are
x [~UMstudent(x) V speaks[~UMspeaksEnglish(x)] and (c) x [UMstudent(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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 Spring '07
 YaoyunShi
 Logic, Fahrenheit, Celsius

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