2022/4/28 21:26 HW #7(SP 2022): CMPSC 360 SP 22, Section 01: Discrete Math/Cs
HW #7(SP 2022)
截止时间 3月17日 23:59 得分 117 问题 11
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最新 尝试 1 669 分钟 77.5，满分 117 分 *
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此测验的分数: 77.5，满分 117 分 * 提交时间 3月17日 23:48 此尝试进行了 669 分钟。
Find the recursive formula for the given series.
(1, 2, 6, 24, 120, 710, ……..)
Let’s consider the index value start from 1, i.e. (a1,a2,a3,………… ).
BASE CASE: a1 =1 relation an=an-1*n
7.5 / 10 分
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2022/4/28 21:26 HW #7(SP 2022): CMPSC 360 SP 22, Section 01: Discrete Math/Cs
Find a closed formula or rule that generates the terms of an integer sequence that begins with the
given number. (Assume: index number n starts with 1) a) (15, 8 , 1, -6, -13, -20, -27, ………)
b) (0, -1/2, 2/3, -3/4, 4/5, -5/6, 6/7, …………)
a) 22-7(n) b)(n-1/n)*(-1)^(n+1)
defined by
a) Find the domain of . b) Find the codomain of . c) Find the image of .
d) Prove or disprove that e) Prove or disprove that
is injective. is surjective.
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2022/4/28 21:26 HW #7(SP 2022): CMPSC 360 SP 22, Section 01: Discrete Math/Cs
c) image is : (-inf, -16) union (-8,-2) d) f is injective
a) Prove that
is surjective and
. Suppose that is injective.
is bijective and
is bijective.
is not injective.
b) Consider
Give an example such that
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2022/4/28 21:26 HW #7(SP 2022): CMPSC 360 SP 22, Section 01: Discrete Math/Cs
You are given the task of painting all n houses indexed in your block.
You can paint each house with one of the three colors blue, yellow, or green, but two neighboring houses cannot be painted with the same color.
(The neighbor of house are houses and houses have only one neighbor.)
You know that the cost of coloring house with color
; the first and last
be the minimum total cost of that house is painted color .
b) Find the recursive relation for and state the initial condition clearly.
is painted and
Part b missing Part a wasn’t proved correctly
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2022/4/28 21:26 HW #7(SP 2022): CMPSC 360 SP 22, Section 01: Discrete Math/Cs
Suppose a function f is mapping from real numbers to real numbers. Find the inverse of functions.
3. h(x) = 4.
Suppose g: A → B and f: B → C where A = {a,b,c,d}, B = {1,2,3}, C = {2,3,6,8}, and g and f are defined by g = {(a,2),(b,1), (c,3), (d,2)} and f =
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2022/4/28 21:26 HW #7(SP 2022): CMPSC 360 SP 22, Section 01: Discrete Math/Cs
{(1,8), (2,3), (3,2)}.
is: {(a,3),(b,8),(c,2),(d,3)}
is: {(2,3),(3,2),(8,1)}
is: {(8,8),(3,3),(2,2)}
答案 1: {(a,3),(b,8),(c,2),(d,3)}
答案 2: {(2,3),(3,2),(8,1)}
答案 3: {(8,8),(3,3),(2,2)}
Let and Find the followings:
(a) (f o g)(x)
(b) (g o f)(x)
(c) (f o g) (-1)
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2022/4/28 21:26 HW #7(SP 2022): CMPSC 360 SP 22, Section 01: Discrete Math/Cs
Prove that if F: is bijective, then function F has an inverse. 您的答案:
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2022/4/28 21:26 HW #7(SP 2022): CMPSC 360 SP 22, Section 01: Discrete Math/Cs
(Optional)
has participated in a chess competition for 11 consecutive weeks.
His winning record is: win at least once a day and win at most 12 times a week.
Prove that has won precisely 21 times in a row during some consecutive days.
Hint: let be the cumulative wins on the day n. Try to prove that for some .
Apply Pigeonhole Principle Th.
If you randomly choose five numbers from the integers 1 through 8, then two of them must add up to 9.
(Apply Pigeonhole Theorem and justify your answer)
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2022/4/28 21:26 HW #7(SP 2022): CMPSC 360 SP 22, Section 01: Discrete Math/Cs
测验分数: 77.5，满分 117 分
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