A set is a collection or list of objects, quantities or numbers with specified properties. The objects that make up a set are called members or elements of the set. Can you name the other elements of the set Q? The following are some few definitions that will enable us to define the elements of sets in problems. An odd number is a number which when divided by two 2 leaves a remainder of one 1. Example: … —5, —3, —1, 1, 3, 5 … 2.
An even number is a number which leaves no remainder when it is divided by two 2. An integer x is said to be a factor of another integer y if x can divide y without leaving any remainder. A prime number is any positive number that is exactly divisible only by itself and one. Example: 2, 3, 5, 7, 11, 13, 17, etc. The prime factors of a number n refer to the factors of n that are prime numbers. Multiple of a number x refers to any number formed when x is multiplied by any integer.
Example: Multiples of 3 are 3, 6, 9, 12, 16, etc. Example 1. List the elements of P and Q. A set P is said to be the subset of the set Q if all the elements of P belong to the set Q. The set of all objects under discussion is called the universe or universal set.
In Example 1. A set, which contains no elements, is called an empty or null set. The complement of a set A is defined as the set of all elements of the universal set u, which are not elements of A. The complement of the universal set is the empty set. We also discussed the connection between two sets. The ideas that we have met so far can be represented very simply by means of a diagram.
This information can be represented diagrammatically. P A diagram like this is called a Venn diagram, after the English mathematician John Venn — Therefore Fig. The power set of S is usually denoted 2S or P S. Power sets are larger than the sets associated with them. Definitions 1. When the elements of a set are arranged in increasing order of magnitude, the first element the least member is called the lower limit whilst the last element the greatest member is the upper limit.
A set is said to be finite if it has both lower and upper limits. In other words, a set is finite if the first and the last members can be found. A finite set is also called a bounded set.
A set without a lower or upper limit or both is called an infinite set. An infinite set is also called an unbounded set. Exercise 1. Write out the following statements in full. Rewrite the following using set notation. Rewrite the following in symbols. Use a Venn diagram to illustrate the following statements: a All good Mathematics students are in the science class, b All bullies are strong people, c All university graduates are wise, d All pastors are compassionate, e All men use guns, f All students suffering from malaria go to the clinic, g All the good students of Mathematics are in the football team, h All students are hardworking.
Consider the following statements p: All scientists are introverts, q: All introverts are anti-social. Draw a Venn diagram to illustrate the above statements. Consider the following statements: a: All my friends like Coca-cola, b: All who like Coca-cola are very studious.
The team is made up of 8 sprinters and 5 hurdlers. He realised that there were 10 athletes in his residence. He checked and found that all the athletes were present. Can you explain it? The solution is much easier using a Venn diagram. We shall use S and H to denote the sets of students who are sprinters and hurdler respectively. The shaded regions Fig. Show all the members of each set.
Solution u A a B a Fig. A Example 1. From Fig. Alternative approach Fig. C P c How many students like only one subject? State the relationship between i and ii.
How many students offer both subject. Since 7 students offer Fig. The Venn diagram is as shown in Fig. Notice that 30 — x students Economics only and 17 — x Government only. Thus, 4 students offer both Economics and Government. In a group of 50 traders, 30 sell gari, and 40 sell rice. Each trader sells at least one of the two items. How many traders sell both gari and rice?
In a class of 42 students, 26 offer Mathematics and 28 offer Chemistry. If each student offers at least one of the two subjects, find the number of students who offer both subjects. Beyond the obvious goals of conceptual understanding and computational fluency, readers are invited to devise mathematical explanations and arguments, create examples and visual representations, remediate typical student errors and misconceptions, and analyze student work.
Introductory discussion questions encourage prospective teachers to take stock of their knowledge of pre-college topics. A rich collection of exercises of widely varying degrees of difficulty is integrated with the text. Activities and exercises are easily adapted to the settings of individual assignments, group projects, and classroom discussions. Mathematics for Secondary School Teachers is primarily intended as the text for a bridge or capstone course for pre-service secondary school mathematics teachers.
It can also be used in alternative licensure programs, as a supplement to a mathematics methods course, as the text for a graduate course for in-service teachers, and as a resource and reference for in-service faculty development. Get BOOK. Mathematics for Secondary School Teachers. Author : Elizabeth G. Focus in High School Mathematics. Authors: Michael Shaughnessy, Beth L. Associated concepts of classical and relativistic mechanics are also discussed with some detail.
Used mainly in solving problems where we have to find the maximization or minimization value as required. This is a textbook on Sampling Rate Conversion. This textbook on Mathematics is intended for 5th graders. It is divided into four terms. It covers topics on mental arithmetic, problem solving, representations, calculations, intervals, laws, operations, economic issues, numeric patterns, output and input values, multiplication, division, data This documents rationalizes the principles of classical signal processing methods and describes how they are used in engineering practice.
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