discrete mathematics set theory questions answers
November 13th, 2020

I have completed one of the exercises and just want to make sure I am getting the correct answers. Some books on elementary(naive) set theory, prefer to introduce sets first and then study logic with the help of associating solution sets to predicates. Prove or disprove the following statement: A*B=B*A. I was able to show graphically that (A-B) union (B-A) do not intersect and same for (B-A)union(A-B) which are graphically equal but I couldn't prove it using procedural version of set definitions and identities. It only takes a minute to sign up. Conclude that $\mid S\mid < \mid P(S)\mid .$ This result is known as Cantor’s theorem. rev 2020.11.24.38066, The best answers are voted up and rise to the top, Mathematics Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us, $E = [-2, 2],\; F = [-3,3],\; A = [0, 1],\;B = [-1,0]$, $(E×F)\setminus(A×B) =\bigl((E\setminus A) × F\bigr)\cup\bigl(E × (F\setminus B)\bigr)$, Welcome to MSE. Now you can proceed much as you did before, applying one of the logical De Morgan’s laws: $$\neg\big(P(x)\land Q(x)\big)\iff\neg P(x)\lor\neg Q(x)\;.$$, That step was fine, except that you were working with an expression that wasn’t quite right to begin with. MathJax reference. In how many ways, sets can be represented? Explanation: Bell numbers give the count of the number of ways to partition a set. C. finite state machines (A\cap B)^c&\iff\neg\big(P(x)\land Q(y)\big)\\ Circularity in formal proof of De Morgan's laws? C. Finite Set The set $\{1, 2, \dots p-1\}$ forms a group under multiplication mod $p$, where $p$ is a prime number. Discrete Mathematics: Set Theory Question? yes that would be great, I too want to know..... Network Sites. Discrete Mathematics: Set Theory Question? It can take a little while to get used to the required precision of mathematical usage, but once you do, you’ll find that it makes things easier to follow.). What kind of overshoes can I use with a large touring SPD cycling shoe such as the Giro Rumble VR? This section focuses on "Sets" in Discrete Mathematics. Provide details and share your research! site design / logo © 2020 Stack Exchange Inc; user contributions licensed under cc by-sa. Making statements based on opinion; back them up with references or personal experience. For those that are countably infinite, exhibit a one-to-one correspondence between the set of positive integers and that set. I went back through my study guide and it had these same steps in a similar exercise, but I missed them in my work. ), $$\begin{align*} Use MathJax to format equations. Let \(f : A \to B\) be an injective (one-to-one) function. Question3: What is Sets in Discrete Mathematics? $Q:$ $R$ is transitive. He had defined a set as a collection of definite and distinguishable objects selected by the mean Represent a subset of the set of positive integers as an infinite bit string with ... complement of the $ith$ bit of the $ith$ string in the list. $(A\cap B)^c$, however, is a set, not a statement: it can no more be true or false than a symphony can be pink. In case that your book is doing the later one, first you should check with truth tables that De Morgan's laws hold in propositional calculus and then you case use it to prove De Morgan's laws for sets. Then you replace logically equivalent statements to arrive at the desired statement. So, that proof is correct, even though you've missed to write $\forall x: x \in \cdots$. Explanation: It is an example of Roster or Tabular Form. Let $G$ be an arbitrary group. This section focuses on "Probability" in Discrete Mathematics. The relation between sets A, B, C as shown by venn diagram is. 250+ Discrete Mathematics Interview Questions and Answers, Question1: What is Discrete Mathematics? a) both iii and iv) b) only iv). Then the number of subsets $S$ (of $C$) which contains $p$ elements and also has the property that $S \cap A$ contains $q$ ... $\begin{pmatrix} m \\ p-q \end{pmatrix} \times \begin{pmatrix} n \\ q \end{pmatrix}$, The domain of the function $\text{ln}(3x^2-4x+5)$ is set of positive real numbers set of real numbers set of negative real numbers set of real numbers larger than $5$, Kenneth Rosen Edition 7th Exercise 2.1 Question 7 (Page No. May someone explain? Both $P$ and $Q$ are false. Let $C$ be a collection of distinct subsets of $A$ such that for any two subsets $S_1$ and $S_2$ in $C$, either $S_1 \subset S_2$ or $S_2\subset S_1$. Featured on Meta A big thank you, Tim Post “Question closed” notifications experiment results and graduation . BARC COMPUTER SCIENCE 2020 NOVEMBER 01, 2020 ATTEMPT, Recent questions and answers in Set Theory & Algebra. 1 U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} A = {2, 4, 6, 8, 10} B = {1, 3, 6, 7, 8} C = {3, 7} (a) Illustrate the sets U, A, B and C in a Venn diagram, marking all the elements in the appropriate places. Which of the following give the count of the number of ways to partition a set? #EM Relations - Is this relation Transitive. Many … Which of the following is the set of positive integers? GO Mechanical. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Only S1 is correct Only S2 is correct Both S1 and S2 are correct None of S1 and S2 is correct, Let (G,*) be a group such that O(G) = 8, where O(G) denotes the order of the group. Represent these two sets in the plane R? Grade 7 Maths Questions on Set Theory With Answers. What have you tried? C. Complement Numbers Consider the following statements about images. Marks 1 More. “Question closed” notifications experiment results and graduation, MAINTENANCE WARNING: Possible downtime early morning Dec 2/4/9 UTC (8:30PM…. The statement $\neg\big(P(x)\land Q(y)\big)$ actually says that it is not the case that $x\in A$ and $y\in B$. Define \(h : 2^B \to 2^A\) as: \(h(D) = \{x \mid x \in A, f(x) \in D\}\), for all subsets $D$ of ... statements is always true? They are denoted by Bn where n is the cardinality of the set. A. unordered Explanation: Sets can be represented in two ways : Roster or Tabular Form and Set Builder Notation, A. Roster Form B. the set of all positive integers How to consider rude(?) 2. Then the sequence $(a_{n})_{n}$ is Unbounded Bounded but does not converge Bounded and converges to $1$ Bounded and converges to $0$, A logical binary relation $\odot$ ... to $A\wedge B$ ? To learn more, see our tips on writing great answers. #DiscreteMaths Relationship between Equivalence classes of an equivalence relationship and partition of a set? The set of all bijective functions on a finite set forms a group under function composition. Indescribability of certain infinite objects. C. the set of all whole numbers B. Is whatever I see on the internet temporarily present in the RAM? Can I run my 40 Amp Range Stove partially on a 30 Amp generator. ... Discrete Mathematics (Past Years Questions) START HERE. Let G be a group of 35 elements. How far did you get? Thanks for contributing an answer to Mathematics Stack Exchange! A. Let $S = \{1, 2, 3,\ldots, m\}, m >3.$ Let $X_1,\ldots,X_n$ be subsets of $S$ each of size $3.$ Define a function $f$ from $S$ to the set of natural numbers as, $f(i)$ is the number of sets $X_j$ that contain the element $i.$ That is $f(i)=\left | \left\{j \mid i\in X_j \right\} \right|$ then $ \sum_{i=1}^{m} f(i)$ is: $3m$ $3n$ $2m+1$ $2n+1$, The number of positive integers not exceeding $100$ that are either odd or the square of an integer is _______ $63$ $59$ $55$ $50$. Showing $(A\triangle B)\subseteq C$ iff $A\cup C=B\cup C$ (using logical equivalence only). A. Babylonians Kenneth Rosen Edition 7th Exercise 2.5 Question 38 (Page No. Which of the following is union of {1, 2, 5} and {1, 2, 6}? These Multiple Choice Questions (mcq) should be practiced to improve the Discrete Mathematics skills required for various interviews (campus interviews, walk-in interviews, company interviews), placements, entrance exams and other competitive examinations. But it really depends on how you define such things. What you want here is, $$\neg P(x)\lor\neg Q(x)\iff x\notin A\lor x\notin B\iff x\in A^c\lor x\in B^c\iff x\in A^c\cup B^c\;.$$. D. None of the above. What's the current state of LaTeX3 (2020)? GO Electronics. Power Numbers The sum of square of the first n natural numbers is given by. C. unordered and ordered Determine which inclusions are true (by justifying) between the sets $(E\setminus A) × (F\setminus B)$ and $(E×F)\setminus (A×B)$. There exist more then one element in G whose order is 1 None of these, Let $n =$ $p^{2}q$, where $p$ and $q$ are distinct prime numbers.

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