# set theory questions

We write sets using braces and denote them with capital letters. This set contains five elements, namely, a, e, i, o, u. N = {1,2,3,…} is the set of counting numbers, or naturals. A set is a collection of objects. A = {1,2,3,…,10} is the set of the first 10 counting numbers, or naturals, B = {Red, Blue, Green} is the set of primary colors, N = {1,2,3,…} is the set of all naturals, and Z = {...,−3,−2,−1,0,1,2,3,…} is the set of all integers. The notion of set is taken as “undefined”, “primitive”, or “basic”, so we don’t try to definewhat a set is, but we can give an informal description, describe important properties of … It is usually represented in flower braces. Definition. Sets, Set Theory - Practice Questions A collection of questions that typically appear on Sets, Set Theory, Union and Intersection of 2 or 3 sets. These short objective type questions with answers are very important for competitive exams as well as Board exams. A - B be the set of people who speak English and not French. 1. (c) The collection of all real numbers x for which: 2x – 9 = 16. Solved Questions: Question 1: If ∪ = {1, 3, 5, 7, 9, 11, 13}, then which of the following are subsets of U. Set Theory Multiple Choice Questions and Answers for competitive exams. C) 300 D) 600 Answer:- Number of people who speak both = 1500 = 800 + 900 – n(H ∩ E) n(H ∩ E) = 1700 – 1500 = 200 So option number (A) is right. A) 200 B) 400 2. A∩B) is simply {2, 4}, The union of sets A and B, written as A∪B, is the set of elements that appear in, The union of A and B (i.e. (b) The collection of all tall people. Now, lets us try doing some questions based on Set Theory. Set theory is a basis of modern mathematics, and notions of set theory are used in all formal descriptions. Well-defined means, it must be absolutely clear that which object belongs to the set and which does not. Therefore, Number of persons who speak both French and English = 15, Therefore, Number of people speaking English only = 57, Number of people speaking French only = 28. Grade 7 maths questions on set theory with answers are presented. We denote the empty set by ∅, or {}. (A ∪B) = 60     n(A) = 27     n(B) = 42 then; Therefore, 9 people like both tea and coffee. The concepts tested include union and intersection of 2 or 3 sets, subsets, proper subsets, and complimentary sets. The Cartesian product of sets A and B, written A x B, is expressed as: A x B = {(a,b)│a is every element in A, b is every element in B}, The Cartesian product of A and B (i.e. A = {a, b, c, d} and B = {1, 4, 7, 9, 10, 12, 23} Give the cardinality of. Set Theory Exercise 1 . Question 1: In a class of 120 students numbered 1 to 120, all even numbered students opt for Physics, whose numbers are divisible by 5 opt for Chemistry and those whose numbers are divisible by 7 opt for Math. Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects. Learn the basic concepts and formulas of Set Theory with the help of solved examples. The language of set theory can be used to define nearly all mathematical objects. A ∩ B be the set of people who speak both French and English. The most natural way to describe sets is by listing all its members. Some common examples of well defined sets: Two sets A and B are said to be equal if and only if both the sets have same and exact number of elements. A∪B) is {1, 2, 3, 4, 5, 6, 8, 10}, The difference of sets A and B, written as A-B, is the set of elements belonging to set A and, The difference of A and B (i.e. Z = {…,−3,−2,−1,0,1,2,3,…} is the set of integers. GMAT Quant | Set Theory Y ou may get one to two questions from sets in the GMAT quant section - in both variants viz., problem solving and data sufficiency. In this article, we have learnt about the different types of sets as well as formulas to solve questions in a simplified manner. These short solved questions or quizzes are provided by Gkseries. Set theory has its own notations and symbols that can seem unusual for many. Give the cardinality of set A and B defined by. Also, the solutions and explanations are included. B - A be the set of people who speak French and not English. We know that number of elements belonging to exactly two of the three sets A, B, C, = n(A ∩ B) + n(B ∩ C) + n(A ∩ C) - 3n(A ∩ B ∩ C), = n(A ∩ B) + n(B ∩ C) + n(A ∩ C) - 3 × 4 ……..(i), n(A ∪ B ∪ C) = n(A) + n(B) + n(C) - n(A ∩ B) - n(B ∩ C) - n(A ∩ C) + n(A ∩ B ∩C), Therefore, n(A ∩ B) + n(B ∩ C) + n(A ∩ C) = n(A) + n(B) + n(C) + n(A ∩ B ∩ C) - n(A ∪ B ∪ C), = n(A) + n(B) + n(C) + n(A ∩ B ∩ C) - n(A ∪ B ∪ C) - 12. A-B) is {1,4}. Here, if and only if means that both parts of the statement ("A = B" and "both sets have the exact same elements") are interchangeable. Take this test to check your understanding of the topic – Sets(Test Name- Sets & Venn Diagram Basic 01). Copyright © Hit Bullseye 2020 | All Rights Reserved, Learn another method to solve questions on Sets: Venn Diagrams, The collection of vowels in English alphabets. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics. {2,4,6,8} = {4,8,6,2} and {2,4,6,8} = {2,4,2,6,8,2,6,4,4}. For example. In this tutorial, we look at some solved examples to understand how set theory works and the kind of problems it can be used to solve. Sample GMAT practice questions from set theory is given below. Note that we could also write, for example, ∅= {x | x ∊N and x < 0} or ∅, The intersection of sets A and B, denoted as A ∩ B, is the set of elements common to, The intersection of A and B (i.e. A very important set is the empty set, or the null set, which has no elements. (e) The collection of all good tennis players. 1 Is each of the following a well-defined set? B = set of persons who got medals in dramatics. C = set of persons who got medals in music. Another example comes from the set of even naturals, which can be described as E = {2,4,6,8,…} = {2x | x ∊ N}. A x B) is {(1,4), (1,5), (1,6), (2,4), (2,5), (2,6)}. Give brief reasons for each of your answers.