Comp Sci 250: Spring 2014
P1.1.1
Homework 1
Due: 02/12/2014
(a) A = cfw_3, 11, 2 elements, A D
(b) B = cfw_1492, 9, 11, 3 elements
(c) C = cfw_5, 11, 1331, 50, 4 elements
(d) D = cfw_1, 3, 5, 7, 9, 11, 6 elements
(e) E = cfw_11, 1 element, E A, B, C, D
(f
Comp Sci 250: Spring 2014
Homework 3
Due: 03/12/2014
P3.5.2 (10XC)
(a) If c is not a multiple of 400, then the number of days in a period c years depends on when the period starts.
The CRT would then suggest an answer of 2800, as we have mod-7 and mod-400
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Exis
Ilan Shenar
HW1
1.1.3
a) cfw_empty, cfw_1, cfw_2, cfw_3, cfw_1, 2, cfw_2, 3, cfw_1,3, cfw_1,2,3
b) cfw_empty, cfw_1, 3, cfw_1,2, cfw_2,3
c) cfw_empty, cfw_1, cfw_2, cfw_1,2
d) cfw_1,2,3
e)
1.2.2
a) If u is a prefix of v than there must be a string w such
Ilan Shenar
HW2
Worked with Nick Hower
2.3.1)
a) cfw_(w,v): (P(w) P(v) R(v,w)
b) cfw_w: : P(w) Q(w)
c) cfw_(w,v): (P(w) P(v) R(v,w) Q(w)
2.3.2)
This tells us that every value of type T shares a particular property. For example, let's say T is of type Red
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CMPSCI 250 Homework #2
Solutions
Throughout this document, the following conventions hold:
The logical operators bind with dierent strength, in the following order (this convention is very common;
learning it will prove helpful):
1. 2. 3. , 4. 5.
This m
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Ru
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HW3
Problem 3.3.3 (10)
For mod 8, 1 if i = 0, 2 if i = 1, 4 if i = 2 and oth1erwise for all i > 2 it is 0, all powers of 2 greater than 2 are
divisible by 8
For mod 9, 1 if i = 0, 2 if i = 1, 4 if
HW4
Ilan Shenar
Collaborated with Nick Hower
Referenced Online Sources
Problem 4.9.1 (10)
Base Case: P(0), when there are zero edges, x = y, and every path has a path so itself, y = x
Assume there is a node 'w' and a path from y to w (y,w). Then, since (x
Ilan Shenar
HW1
1.1.3
a) cfw_empty, cfw_1, cfw_2, cfw_3, cfw_1, 2, cfw_2, 3, cfw_1,3, cfw_1,2,3
b) cfw_empty, cfw_1, 3, cfw_1,2, cfw_2,3
c) cfw_empty, cfw_1, cfw_2, cfw_1,2
d) cfw_1,2,3
e)
1.2.2
a) If u is a prefix of v than there must be a string w such
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CS 250
Homework 5
Problem 9.8.4 (5)
Proof by Induction:
For n=0: Impossible, since we need at least 2 nodes
For n=1: Impossible unless s = t is possible, this is not stated so this is assumed as impossible.
Base Case: For n=2: Two nodes s and t and 1 edge
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In Excursion 1.3 of the textbook I tell a story about how mathematical proof works in the real
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