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. In a class of 42 students each student studies either Economics or Accounting or both. If 12 students study both subjects and the number of students who study Accounting only is twice that of those who study Economics only, find how many students study i Economics, ii Accounting.
The required shaded regions are as shown in the Venn diagrams below. Of these, 86 play table tennis, 84 play football and 94 play volleyball; 30 play table tennis and volleyball, 34 play volleyball and football and 42 play table tennis and football. Each student plays at least one of the three games and x students play all three games.
If x is the number of V 94 students who play all three games, then Fig. Each student offers at least one subject. Find the number of students who offer: a Chemistry only, b only one subject, c only two subject.
Each of these members undertakes at least one of the activities. The number of people who go to school only is the same as the number who engages in Trading only. Use the information to find the number of people who a undertake all the three activities, b go to school only. Thus, the number of members who undertake all the three activities is 8.
The following table gives further details of the subjects studied. If the number of students who study only Physics is equal to that of those who study only Chemistry, Illustrate the given information on a Venn diagram and find the number of students who study i Only Physics, ii Chemistry, iii Only one subject.
Mathematics, English and Life Skills books were distributed to 50 students in a class. Find the number of students who had: a all three books, b exactly two of the books, c only Life Skills books. June There are 30 students in a class.
Find Q. A survey of traders in a market shows that 90 of them sell cassava, 70 sell maize and 80 sell yam. Also, 26 sell cassava and maize, 30 sell cassava and yam and 40 sell yam and maize. Each of the traders sells at least one of these crops.
There are boys in a sports club. Each boy plays at least one of the three games. In a class of 52 students, 34 offer Mathematics, 31 offer Chemistry and 36 offer Physics. Each student offers at least one of the three subjects. It's an excellent way to prepare your child for college-level math courses. Our projects explore and analyze how curriculum decisions are made in K—12 mathematics programs, provide resources that Chegg Solution Manuals are written by vetted Chegg experts, and rated by students - so you know you're getting high quality answers.
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The textbook example illustrated the "random sampler" in which a sample of 10 US high school students has been selected and their The math courses offered during high school can be extremely diverse, as each student will come in with a different mathematics background and different mathematics goals.
Sign in with Microsoft. Another feature is that each chapter has an extensive collection of exercises. It is important that students have several exercises to practice. This book is therefore designed to help students to: 1 acquire the basic skills and understanding which is vital to examination success. I have gone to great lengths to make this text both pedagogically sound and error-free.
If you have any suggestions, or find potential errors, please contact the writer at akrongh yahoo. I am also grateful to Prof. Jackson Professor of Statistics of Methodist University College Ghana, for reading a draft of the book and offering helpful comments and suggestions.
I am also indebted to Nana Owusu Mensah Essel who assisted me greatly by spending much time in editing every single chapter of this book. The publication of this book could not continue without the advice and persistent encouragement of Mr.
I would like to thank Mr. Salifu Addo and Mr. Adolf Hansen for reading through some parts of the draft of this book and for making valuable suggestions for its improvement. Finally, my sincere gratitude goes to Mr. Ludwig Hesse Department of Urban Roads, Accra for their moral support, encouragement and for providing professional guidelines. Binary Operations Relations and Functions Quadratic Functions Polynomial Functions Rational Functions Indices and Logarithmic Functions Experimental law Binomial Theorem Linear Programming Coordinate Geometry Straight Lines Coordinate Geometry Circles
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