Practical Problems On Union And Intersection Of Two Sets
Chapter Name : Sets |
Sub Topic Code : 104_11_01_12_01 |
Topic Name : Practical Problems On Union And Intersection Of Two Sets |
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Sub Topic Name : Practical Problems On Union And Intersection Of Two Sets |
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Introduction
Sets are a collection of objects of a particular kind, such as a pack of cards, a crowd of people, a cricket team, etc. In mathematics also, we come across collections, for example, of natural numbers, points, prime numbers, etc. When a set contains a distinct number of elements in it, we call it a finite set else, it’s called an infinite set. Operations like union, intersection, difference and complement can be performed on two or more sets.
Pre-Requisites:
• Definitions of Sets • Operations on Sets
Activity:
Use different colored marbles in your school/home and put them into different bowls. Then, perform different operations on the marbles by assigning a particular colored group of marbles to a set. Take union, intersection, difference and complement of the sets.
Real Life Question:
In a school with 40 students, 29 take up chemistry,14 take up English Composition and 5 take up both these classes. How many students take neither English Composition nor Chemistry?
Key Words / FlashCards
| Key Words | Definitions (pref. in our own words) |
|---|---|
| Set Theory | Set theory is the branch of mathematics that studies sets, which are collections of objects. |
| Union of Sets | In set theory, the union (denoted by ?) of a collection of sets is the set of all distinct elements in the collection. |
| Intersection of Sets | In mathematics, the intersection (denoted as ?) of two sets A and B is the set that contains all elements of A that also belong to B (or equivalently, all elements of B that also belong to A), but no other elements. |
| Complement of Set | In set theory, a complement of a set A refers to things not in (that is, things outside of) A. |
Learning aids / Gadgets
| Gadgets | How it can be used |
|---|---|
| Marbles | Use different colored marbles to perform different set operations practically. |
Real life uses :
Division of your father’s salary to pay different bills like grocery bill, electricity bill, shopping bills etc is basically performing different set theory operations on the total salary.
Places to visit :
Divide different cutlery items in your kitchen according to their use like forks and spoons can be used for eating, plastic and glass plates can be grouped together, different knives can for another set. Thus, divide the kitchen cutlery into different functional collections of sets.
Practical examples around us
| Examples | Explainations |
|---|---|
| Division of chocolates | When a relative comes home and gets you chocolates you divide them into groups so that your brother(s)/sister(s) gets an equal share of different varieties. This is also a division of sets into smaller subsets. |
What you learn in Theory:
Performing different operations like union, intersection, difference and complement on sets.
What you learn in Practice:
To apply set theory to solve different practical problems in your daily life.