Set notation powerpoint presentation grade 10

Set notation and Venn diagram

1. Starter Sort the numbers 1 – 10 into this Venn diagram. Even (A) Square (B) 1 2 3 4 5 6 7 8 9 10  

2. Sets come with strange notation, but a set is just a word for a collection of things. Each thing in a set is called an element or member . Capital letters represent a set, and lower case letters represent elements. Notation is the set of… is an element of is not an element of the number of elements in set the universal set or the empty set (a set containing no elements)  

3. We can describe sets using numbers and symbols. If a set is described using numbers and symbols, work out what the description means in words before you start working with the set. describes the set of negative numbers. describes the set of coordinates that lie on the line .   The colon means ‘such that’

4. Examples List the members of if is the set of numbers , such that is less than Elements of must be in the universal set So List the members of if List the members of if No elements of fit the definition of an element of , so is empty.   Task – complete the set notation worksheet.

5. Answers   1. a)   b) i ) ii) iii) iv)   c) i ) ii) iii) iv) 2. a) i ) ii) iii) b) i ) ii)  

6. B A B A B A The intersection is where two sets overlap. This means A and B . If you put two sets together, you get the union . This means A or B . The complement of A is the region that is not A. This means not A . OR rule AND rule Venn diagrams are can be used to show sets and when they overlap.

7. Use your pieces of tracing paper to correctly shade the Venn diagrams. Don’t forget to keep looking at that exam question too 

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10. Task Complete the worksheet on set notation and Venn diagrams. Remember: if it’s tricky, draw a piccy! (ideally a Venn diagram)

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13. Subsets is a subset of  all of the elements of set are also in set is a proper subset of  is a subset of , but is not equal to is not a proper subset of  some elements of are not in   For all sets: The empty set is a subset of any set, i.e. for any set , 2. Every set is a subset of itself, i.e. for any set , For any two sets and , if and , then  

14. Examples 1. List the subsets of 2. List the proper subsets of   Remember to include the empty set and set itself in the list   Proper subsets of include the empty set, but not set itself  

15. Your Turn The diagram shows the relationship between four sets , , and . Each area of the diagram contains at least one element.   a) State whether each of the following statements is true or false. i ) ii) iii) iv) v) vi) vii) viii) b) Copy the following statements and complete them by placing either or in each of the gaps. i ) ii) iii) iv) v) vi)  

16. Your Turn The diagram shows the relationship between four sets , , and . Each area of the diagram contains at least one element.   a) State whether each of the following statements is true or false. i ) ii) iii) iv) v) vi) vii) viii) b) Copy the following statements and complete them by placing either or in each of the gaps. i ) ii) iii) iv) v) vi)          