Skip to main content
CIT 5920
Sli.do Ed Discussion PrairieLearn Panopto Gradescope Toggle Dark/Light/Auto mode Toggle Dark/Light/Auto mode Toggle Dark/Light/Auto mode Back to homepage
  1. How to Communicate Formally with Discrete Math
  2. /
  3. Notes
  4. /
  5. Sets Relations Functions Student Questions Original
Edit page

Sets Relations Functions Student Questions Original

So 0 is part of N, but 0 is NOT part of N-star? Would 1.0 be a rational number? When do we use “=“ vs “three line equal” sign to indicate equivalence? Can we use the vertical bar to represent “such that”? I think there are two different notations for a subset Is the subset notation not underlined? It is in the lecture notes so if ACB means every element of A is an element of B, it does not mean that every element of B belongs to A? just a one way relationship? is the subset with and without the line underneath really interchangeable? I thought one means the two sets can be equal didn’t you say an item inside a set can also be a set? what if the pattern is unclear? does question have to state the pattern? Is it possible for 4.5 to be in the set {1, 2, 3, …, 5}? Can ellipses be used in set roster notation if we specify the conditions? Especially for non-number sets like colors (colors of the rainbow) so as long as a pattern can be observed and followed, the ellipsis can be used in set roster? When you said ‘between’, is it inclusive

We established that set N has only numbers from 0,1,2,3. For the Let Odd equals question don’t we only have two odd numbers from set N? That is 1 and 3? does {} mean anything? or was this a trick option
how many elements does ｛｛｝｝have What about {{{}}}? what is the subset of {{}} 1 anything not separated by commas within a {}, even if its {{}} or {{{}}} is 1 element It has one element?
Can we increase the temperature Is {{7}} a subset of x? in this case where there is a subset e.g., {7}, can we say 7 is a subset of {7}? Yes So ‘syntactic problem’ and ‘incorrect statement’ are two types of ‘False’? Do we need to specify them in the exam? 7 is not even a set We can never extract 7 out of a { {7} } right? {7} can not be a subset of { {7} } once a group of element is clumped into a subset, all of the elements are now forever bonded together? i.e., {1,2,{3,4,5}} like 3,4,5, are considered one In this class, can a Venn Diagram be a way of mathematical proof? The lecture notes include difference, would we need to know that as well? For A u B: would x belongs to A or x belongs to B be a way of writing it as well? isn’t A ∪ B = {x ∈ U|x ∈ A or x ∈ B}? For complement can I also write x belongs to B too or would that be redundant? If U is not defined in a question, can we just say AUB={x | x belongs to A or x belongs to B}? how is B\A different from complement of A? or are they the same Can you write complement as A’ also?

How do we get the complement when the set U is not specified? e.g) Odd’s complement. N-Odd, Z-Odd, R-Odd, or C-Odd? Would {1,2,3,3,3,3,4,5} still be a union of the sets? but I think two options are indeed the same one, and there is only one set after union, so I choose one which covers the other Wouldn’t the second option correct as well? for question 5, should N equal t {0,1,2,3…} odd numbers can be negative, right? Here, we just define them to be in the set of natural number. Where can we find the lecture notes for this lecture Can we get the slido questions after class? one screen is not working is (A U B) n C = A n (B n C) correctly associative Subtraction is nonassociative? Division? does the absorption law apply in regular arithmetic or is it just apply in boolean algebra? 2^n? 2^(Card(s)) 2 to power of number of elements in power set 2^n does cardinality account for double elements in the set –> so is card({1, 3, 3, 4}) = 3 or 4 isn’t cardinality just number of unique elements in a set is cardinality of power set always 2 to the power of the previous set? because you can be asked what is cardinality of a power set of a power set and so on |A||B|

commutative is just flipped? as long as all operators are same Commutative property != Commutative laws? Can something be showing the commutative AND associative law at same time? because that’s the third option right? associative = move parenthesis around each sets , commutative = flipping the sets (but both requires same operators) right? Shouldn’t it be {(1, a), (1, b), (2, a), (2, b)}? is it empty due to the absorption law? order only matters in the parentheses then? in matrix, the order also matters why A₁ × A₂ × A₃ is not {((1, a), x),((1, b), x)} ? if you try to find a Cartesian product of a Cartesian product produced set, would you then need to nest parentheses? for the previous Q, why did you say it does not contain all of A (option c)? so if you have unknown elements, it override the rule of order doesn’t matter for sets? for questions that we did on slido. Will we get a pdf version of them? we can just list one example, right (e.g., for i =2)? we can just list one example to prove that C is incorrect, right (e.g., for i =2)? Why can we choose B even after being told that Aᵢ for i = 1, 2, … n are non-empty sets? When the order is 2,4,6,8,10, how can the answer be a5 = 12? Wouldn’t 12 be a6? How can A be partitioned into P? can ai be any number since order does not matter in sets? Because if an empty set can be a result of partitioning, then there will be finite partitions? why it’s not valid since {} u A = A and {} n A = {}? Can you repeat your explanation why option 3 is wrong? A = A1 + A2 + A3 why write aRb instead of (a,b) ∈ R a relation can be both symmetric and anti-symmetric? such as {(a,a), (b,b)}?

can you have a relation over the same set? wouldn’t it not be reflexive because state A could border state B but state C might not border state A right? you can prove symetric with two tuples such as (NJ,PA) (PA, NJ) right? Every element is a subset of itself. So all the sets are reflexive in nature??? Not really. If relation means >, thus you can never find x>x. So for this condition, it is not reflexive. Can you explain what symmetric and anti-symmetric are you would use 3 tuples to prove transitive like (a,b) (b,c) (c,a) right? are relations always between 2 values? does anti-symmetric in this case means “if PA next to NJ and NJ next to PA, then it must be the case that PA = NJ” (which is not true)? So it is both reflexive and symmetric Does it mean if one is symmetric, it must be reflexive as well? symmetric can be proven with 1 or 2 tuples while reflexive can only be proven with 1 tuple. This makes the difference right? For this question"Does it mean if one is symmetric, it must be reflexive as well?" would it be that if something is reflexive it must be symmetric, but not necessarily the other way around? range is the subset of the codomain, right? so we need a 1-to-1 matching between x and y to be a function countries is input and capital is output? as denoted by the statement countries to capital? So does this mean that y will always have the same or greater number of elements than x? can you nest functions? in which a function(a) becomes an input for another function(x) and another function(y) becomes the output for that function(x) What if two different elements of x are related to the same element of y? So all the elements in X should be mapped to one of the elements in Y and it is no hard rule that all elements in Y should be mapped. Is that correct? Can it be one-one when there are more elements in y than in x? Will we need to prove a function is bijective by first proving it is both surjective and injective in the future? so if a function is injective, we say there is definitely an inverse function? Is the function f(x) = x^2 from the set of integers to the set of integers onto? what makes it important to identify these 3 properties? in algebra you can have f(x) where x can equal to two values, would that be different from discrete math context? In the previous question, does it not matter that there was no arrow (no order for the pair)?