Solved Examples on A intersection B
Example 1: Let’s consider two sets, Set X and Set Y. Set X consists of {apples, bananas, oranges, grapes}, and Set Y consists of {bananas, grapes, peaches}. Find the intersection of Set X and Set Y
Solution:
To find the intersection of Set X and Set Y, we look for elements that are common to both sets. In this case, the common elements are “bananas” and “grapes.”
Set X ∩ Set Y = {“bananas”, “grapes”}
Therefore, the intersection of Set X and Set Y is {“bananas”, “grapes”}.
Example 2: Imagine you’re at an ice cream parlour. You have a 1/4 chance of choosing chocolate ice cream, a 1/3 chance of adding choco flakes, and a 1/2 chance of adding whipped cream to your ice cream. What’s the probability that you choose chocolate ice cream and add whipped cream?
Solution:
Probability of choosing chocolate ice cream = P(A) = 1/4
Probability of adding whipped cream = P(B) = 1/2
P(A ∩ B) = P(A) ✕ P(B)
= (1/4) ✕ (1/2)
= 1/8
Example 3: Consider two sets, Set A and Set B. Set A contains {oranges, pears, strawberries, kiwis}, and Set B contains {pears, kiwis, bananas}.
Solution:
To find the intersection of Set A and Set B, we’ll identify elements that are common to both sets. In this case, the common elements are “pears” and “kiwis.” Set A ∩ Set B = {“pears”, “kiwis”} Therefore, the intersection of Set A and Set B is {“pears”, “kiwis”}.
Example 4: Consider you have at a set of pens . You have a 1/8 chance of choosing black pen, a 1/2 chance of choosing blue pen, and a 1/5 chance of choosing designer pen cap. What’s the probability that you choose blue pen with designer pen cap?
Solution:
Probability of choosing blue pen = P(A) = 1/2
Probability of choosing designer pen cap = P(B) = 1/5
Using independence:
P(A ∩ B) = P(A) ✕ P(B)
= (1/2) ✕ (1/5)
= 1/10
Example 5: Let’s consider two sets, Set A and Set B. Set A consists of {red, yellow, orange, black, pink} and Set B consists of {pink, white, golden}. Find A intersection B.
Solution:
To find the intersection of Set A and Set B, we look for elements that are common to both sets. In this case, the common element is pink.
Set A ∩ Set B = {pink}
Therefore, the intersection of Set A and Set B is {pink}.
A∩B Formula
A Intersection B Formula is an important mathematical formula used to find the common region between two sets A and B. A intersection B formula in mathematical notation is represented with the Intersection Symbol “∩” i.e., A∩B. The Intersection symbol when used with different sets is used to denote the intersection of those selected sets. This can be represented as (A ∩ B) represents that both set A and set B occur at the same time. In other words, (A ∩ B) represents elements from both set A and set B.
In this article, we will learn A intersection B Formula including the Venn diagram for A intersection B and the intersection of three sets A, B, and C in detail to understand the concept better along with some solved examples and practice problems.
Table of Content
- What is A Intersection B?
- Probability of A Intersection B
- A Intersection B Intersection C
- A Intersection B Union C
- Solved Examples on A intersection B