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
Sep 17, 20 03:57 PM
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