College Math

College Math Study Guide

The first possibility gives us a false conclusion, while the second possibility gives us a true conclusion. So, it should be noted that when we get a case when true premises do not lead to a true conclusion, the argument is known as invalid. 6.11 Sets We have covered some basic concept building about sets in the first chapter of the book. Now, we take it forward and understand some related concepts and application of sets. Before that, let us revise some of the basics and operations about sets. A set can be defined as the collection of elements. For instance, number of students in a class, hearts in a deck of playing cards, etc. Sets are denoted by capital letters like A, B, C, and so on. The objects in the sets are known as elements and are represented by small letters like a, b, c, etc. If we have a set A, and a is an element in a set, then we write it symbolically as: a ∈ A and, if we have to write that a does not belong to the set A, then we write it as: a /∈ A. The unique characteristic of all elements in a set is that they have some similarity in appearance of purpose. For instance, {2, 4, 6, 8} represents the set of all one-digit even numbers, and {a, e, i, o, u} represents the set of all vowels in English. Sets are denoted by a letter. The set of all positive numbers less than 10 is denoted by S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and the set of all odd numbers less than 10 is denoted by T= {1, 3, 5, 7, 9}. In this case, T is known as the subset of S, since all the elements in the set T is present in the set S. another way to describe a set is by using a set-builder notation . For instance, the set {1, 3, 5} in a set-builder notation is written as {x l x is an odd number between 0 and 6}. A set-builder notation is read as follows:

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