Definition:
Given two sets A and B, the intersection is the set that contains elements or objects that belong to A and to B at the same time.
We write A ∩ B
Basically, we find A ∩ B by looking for all the elements A and B have in common. Next, we illustrate with examples.
Example #1.
To make it easy, notice that what they have in common is in bold.
Let A = { 1 orange, 1 pineapple, 1 banana, 1 apple } and B = { 1 spoon, 1 orange, 1 knife, 1 fork, 1 apple }
A ∩ B = { 1 orange, 1 apple }
Example #2.
Find the intersection of A and B and then make a Venn diagrams.
A = { b, 1, 2, 4, 6 } and B = { 4, a, b, c, d, f }
A ∩ B = { 4, b }
Example #3.
A = { x / x is a number bigger than 4 and smaller than 8 }
B = { x / x is a positive number smaller than 7 }
A = { 5, 6, 7 } and B = { 1, 2, 3, 4, 5, 6 }
A ∩ B = { 5, 6 }
Or A ∩ B = { x / x is a number bigger than 4 and smaller than 7 }
Example #4.
A = { x / x is a country in Asia }
B = { x / x is a country in Africa }
Since no countries in Asia and Africa are the same, the intersection is empty.
A ∩ B = { }
Example #5.
A ∩ B = { }
We write A ∩ B ∩ C
Basically, we find A ∩ B ∩ C by looking for all the elements A, B, and C have in common.
A = { #, 1, 2, 4, 6 }, B = { #, a, b, 4, c } and C = A = { #, %, &, *, $, 4 }A ∩ B ∩ C = { 4 , # }
The graph below shows the shaded region for the intersection of two sets
Nov 18, 20 01:20 PM
Top-notch introduction to physics. One stop resource to a deep understanding of important concepts in physics
Basic math formulas
Algebra word problems
New math lessons
Your email is safe with us. We will only use it to inform you about new math lessons.