补丁
- 2025年6月14日07点55分 - 由Katana发现的第
6题拼写错误
第一题
Which of the following are correct:
第二题
Neither A or B is right means：
A and B are both wrong
A is right and B is wrong
A and B must have one wrong
A and B can have one wrong
第三题
let set , which of the following are not partition of .
第四题
Prove by induction on that, for all n:
第五题
let , proof by case that that is divisible by 3, (i.e )
第六题
Definitions:
- Let be the set of all 4-digit student number. (where 0001 is a valid sutdent number)
- Let be the student's exam time slot, chosen from the set:
{morning, afternoon, evening}.
(a) What is the cardinality of ？
(b) Define a function that is subjective, but not injective. Give justification that your
(c) Let be defined as , (. Determine whether is injective, surjective, neither, or bijective.
第七题
Select all the correct statement:
第八题
Show that
1.
第九题
Let be a student which study FIT 1058
Turn this predicate logic, in a “Universal quantifier”
第十题
a) Find the Recurrence relation for , where
b) Calculate the Big O for
第十一题
Use the Extended Euclidean Algorithm to show that 24 and 11 are co-prime.
第十二题
Let be Euler’s totient function, which counts the number of positive integers less than or equal to that are relatively prime to . Compute . Given .
第十三题
There are 15 student study FIT 1058 this semester.
You don’t need to compute the exact value for the following question.
a) Rebecca decide to randomly pick 3 students, and sign their final exam to Fail. Each student have a equally chance, how any combination can Rebecca pick from?
b) Alexey decide to randomly give 3 prices to the students (one student can be more than one prices). How many ways Alexey can give out his price?
c) Graham decide to randomly tell a student the exam answer student during exam every 30 mins, (5 students in total). Notice the order does mater, how many ways Graham can share the exam answer?
第十四题
Given and
a) Find
b) Find
第十五题
A student enters an exam without any preparation and decides to guess all 20 multiple-choice questions (1 mark per question). The probability of guessing a question correctly is 0.20. He answers the questions sequentially, from Question 1 to Question 20.
You don’t need to compute the exact value for the following question.
a) What is the probability that his first correct answer occurs on Question 6?
b) Given that a student is randomly guessing on a multiple-choice test, which probability distribution best models the number of attempts until his first correct answer?
Uniform Distribution
Binomial Distribution
Poisson Distribution
Geometric Distribution
c) State the binomial distribution for this student's score, and calculate the expected score and standard deviation.
第十六题
The graph G has 6 vertices with degrees 2,2,3,4,4,5. How many edges does G have? Could G be planar? If so, how many faces would it have. If not, explain.
第十七题
I’m thinking of a connected planar containing 12 faces. Seven are triangles and four are quadrilaterals. The planar has 11 vertices including those around the mystery face. How many sides does the last face have?
Prove that there are exactly 5 regular polyhedra.
这题难度超标了，想做的同学可以去看乐乐同学对Graph的笔记。传送门 → 这里就不算在考试里了
