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. We next 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
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Oct 24, 16 06:10 PM
Straightforward proof of the law of sines. Easy to follow and understand