Solving Set Union: Find $n(A \cup B)$
This problem requires calculating the number of elements in the union of two sets, denoted as $n(A \cup B)$. We are given the counts of elements in each set and their intersection.
Given Information
- Number of elements in set A: $n(A) = 28$
- Number of elements in set B: $n(B) = 35$
- Number of elements common to both A and B (Intersection): $n(A \cap B) = 12$
Union Formula
The formula to find the number of elements in the union of two sets A and B is:
$n(A \cup B) = n(A) + n(B) - n(A \cap B)$Calculation
Substitute the given values into the formula:
- $n(A \cup B) = 28 + 35 - 12$
- $n(A \cup B) = 63 - 12$
- $n(A \cup B) = 51$
Result
Therefore, the number of elements in the union of sets A and B is 51.
Important Questions from Set Theory and Venn Diagram (Notes)
A student is free to choose only Chemistry, only Biology or both. If out of $32$ students, Chemistry has been chosen by $16$ and Biology by $25$, then how many students have chosen Biology but not Chemistry?
- Fourteen of the students in a class are girls. Eight students in the class wear blue shirts. Two are neither girls nor wear blue shirts. Five students who wear blue shirts are girls. How many students are there in the class?
- In a group of 44 players, 26 play hockey, 24 play football and 24 play cricket. Eight of them play both hockey and football, 12 play both football and cricket, and 5 play all the three games. How many play both hockey and cricket?
- In a group of students, 30% play only cricket, 20% play only football and 10% play only basketball. 20% of the students play both football and cricket, 15% play both basketball and cricket, 10% play both football and basketball. 15 students play no games, while 5% of the students play all three games. What is the total number of students?
- Which of the following statements are true ?
A. Set A = {x : x $\in$ R and 2 < x < 3} is a null set.
B. Set A = {x : x $\in$ R and 2 < x < 4} is a singleton set.
C. Set A = {x : x $\in$ R and 1 < x < 9} is an infinite set.
D. Set A = {x : x $\in$ R and 1 < x < 9} is a finite set.
E. Set A = {a, b, c, d, e} and B = {c, d, a, e, b} are equal sets.
Choose the correct answer from the options given below :
