Lecture 1 Set Operations & Applications Lecture 1 Set Operations & Applications ITP3902 Discrete Mathematics & Statistics Page 1 Lecture 1 Set Operations & Applications Sets and elements • A Set is a collection of objects. Often the objects in a set have similar properties. • Set theory is the foundation of modern mathematics. Element • The objects in a set are called its elements. • If a is an element of set A‚ it belongs to A and is written as a A. • If a does not belong to A‚ we write
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first term 2 and third term 32. Find the common Ratio. ix) Find the sum of the first 12 terms for the same sequence. x) There are 25 students in a class. 17 study French‚ 12 study Malay and 10 study both languages. Show this information on a Venn diagram. xi) How many study French only xii) Malay or French or both xiii) study neither xiv) study one or the other but not both xv) The measurements of a length and width of a rectangular kitchen are 5.34m and 3.48m respectively. Calculate in
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Venn Diagram A Venn diagram usually is a drawing‚ in which circular areas represent groups of items sharing common properties. The drawing consists of two or more circles‚ each representing a specific group or set. This process of visualizing logical relationships was devised by John Venn (1834-1923). Each Venn diagram begins with a rectangle representing the universal set. Then each set of values in the problem is represented by a circle. Any values that belong to more than one set will
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schedule of the final exam will be common for all the sections. Course Content: Topic name Topic details Weeks Set Theory Definition of sets‚ representation‚ classification‚ set operations‚ Venn diagrams‚ Venn – Euler Diagram to solve practical problems 1 Number system Types of numbers‚ modulus‚ Interval diagrams‚ Interval notations‚ solving set operations using interval notations. 2 Partial Fractions‚ Surds‚ Quadratic equations Proper and improper fractions‚ partial fraction method‚ finding roots
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Similarities and Differences Comparing is the process of identifying similarities and differences between ideas or things. A variety of strategies can be used when designing comparison activities. We will discuss sentence stems‚ Venn diagrams‚ double bubble diagrams and comparison matrices. Sentence Stem Comparisons This strategy can be used to have the students compare and contrast people‚ characters‚ places‚ events‚ concepts or processes. The comparisons can be general or specific. Marzano’s
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August 2026 Activities Activity One: First Reading Read the story Can you make any links to the poem we have already studied? What are some differences? Complete a VENN diagram using TWO pages of your book: Close read the short story together Activity Two: Preliminary Activities 1. Re-tell the story in your own words (don’t look at the story)- what words or phrases can you remember? 2. Read the story again. 3. Summarise the short story in exactly 19 words. 4
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those features are “shared derived characters”. When we do studies in comparative anatomy‚ and find different numbers of shared derived characters exist between different groups‚ we can draw a diagram of branching lines which connect those groups‚ showing their different degrees of relationship. These diagrams look like trees and are called "phylogenetic trees" or "cladograms" (CLAY-doe-grams); see examples provided by your teacher. The organisms are at the tips of the stems. The shared derived features
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a lesson using Venn diagrams. Venn diagrams are an example of a graphic organizer and Venn diagrams are great tools for comparing and contrasting because they provide a quick way to see the similarities and differences of the topics. A learning objective for second grade students is to compare and contrast works by different authors in the same genre or regarding the same thing. (Perma-Bound) One way I can introduce the Venn diagram to my students is by drawing a large diagram on the board in
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Language Arts Literature Regions/Cultures Grades K - 2 3 - 5 Brief Description Use a Venn diagram to compare two stories -- the fairy tale Cinderella and the native American Cinderella story‚ The Rough-Face Girl. Objectives Students will understand that there are similarities as well as differences between cultures. see that literature‚ reading‚ and the passing down of stories is common to all peoples. construct a Venn diagram to help them compare and contrast the stories; identify qualities of the stories
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1. a) In the diagram Shown above‚ the Universal set‚ (U)‚ represents all the students in a class. The set M represents the students who take Music. The Set D represents the students who take Drama. If 24 students take Music‚ calculate i. the number of students who take BOTH Music and Drama ii. the number of students who take Drama ONLY. (4 marks) b) A straight line passes through the point P(‑3‚ 5) and has a gradient of i. Write down the equation of this line in the form y = mx + c
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