Mathematics - 0580 CIE

Sets

Gbogbo ọrọ náà

A set is simply a collection of things, and once you have a precise way to talk about collections you can describe almost anything in mathematics: the factors of a number, the solutions of an equation, the students who study both French and Spanish. Sets give you the exact language, and Venn diagrams give you the picture.

In this lesson you will learn the symbols mathematicians use for sets, how to read and write them, and how to draw and interpret Venn diagrams. You will work with the union and intersection of sets, the complement of a set, and (for Extended) the relationships between sets such as subsets. These tools reappear later in probability, so they are well worth mastering.

Ebumnobi

Understand and use set language, notation and Venn diagrams to describe sets.
Understand and use set language, notation and Venn diagrams to describe sets and represent relationships between sets. (Extended only)

Akọmọ Ojú-ẹkọ

Sorting things into groups and asking what they have in common is one of the most natural things we do. Set notation makes that precise, and the same diagrams you meet here are used directly in probability to organise outcomes. A little fluency with the symbols goes a long way.

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Ayẹwo Ẹkọ

Ekele diri gi maka imecha ihe karịrị na Sets. Ugbu a na ị na-enyochakwa isi echiche na echiche ndị dị mkpa, ọ bụ oge iji nwalee ihe ị ma. Ngwa a na-enye ụdị ajụjụ ọmụmụ dị iche iche emebere iji kwado nghọta gị wee nyere gị aka ịmata otú ị ghọtara ihe ndị a kụziri.

Ị ga-ahụ ngwakọta nke ụdị ajụjụ dị iche iche, gụnyere ajụjụ chọrọ ịhọrọ otu n’ime ọtụtụ azịza, ajụjụ chọrọ mkpirisi azịza, na ajụjụ ede ede. A na-arụpụta ajụjụ ọ bụla nke ọma iji nwalee akụkụ dị iche iche nke ihe ọmụma gị na nkà nke ịtụgharị uche.

Jiri akụkụ a nke nyocha ka ohere iji kụziere ihe ị matara banyere isiokwu ahụ ma chọpụta ebe ọ bụla ị nwere ike ịchọ ọmụmụ ihe ọzọ. Ekwela ka nsogbu ọ bụla ị na-eche ihu mee ka ị daa mba; kama, lee ha anya dị ka ohere maka ịzụlite onwe gị na imeziwanye.

If A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, what is A ∩ B? A. {1, 2, 5, 6} B. {3, 4} C. {1, 2, 3, 4, 5, 6} D. { } Answer: B
If A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, what is A ∪ B? A. {3, 4} B. {1, 2, 5, 6} C. {1, 2, 3, 4, 5, 6} D. {1, 2, 3, 4, 4, 5, 6} Answer: C
The universal set is {1,2,3,4,5,6,7,8} and A = {2,4,6,8}. What is A'? A. {1, 3, 5, 7} B. {2, 4, 6, 8} C. {1,2,3,4,5,6,7,8} D. { } Answer: A
Which symbol means 'is an element of'? A. ⊆ B. ∪ C. ∈ D. ∩ Answer: C
If A = {2, 4} and B = {1, 2, 3, 4, 5}, which statement is true? A. A ∪ B = {2, 4} B. A ⊆ B C. B ⊆ A D. A ∩ B = { } Answer: B