Solving for Students Who Like At Least One Drink
This problem involves finding the total number of students who like cold drinks, milkshakes, or both, based on survey data. We can use the Principle of Inclusion-Exclusion.
Defining Sets and Given Values
- Let $C$ be the set of students who like cold drinks.
- Let $M$ be the set of students who like milkshakes.
- Number of students who like cold drinks: $|C| = 140$.
- Number of students who like milkshakes: $|M| = 120$.
- Number of students who like both cold drinks and milkshakes: $|C \cap M| = 80$.
- Total students surveyed: 200 (This information is not directly needed for calculating the union but provides context).
Applying the Inclusion-Exclusion Principle
We need to find the number of students who like at least one of the drinks, which is represented by the union of the two sets, $|C \cup M|$. The formula is:
$ |C \cup M| = |C| + |M| - |C \cap M| $Calculation
Substitute the given values into the formula:
$ |C \cup M| = 140 + 120 - 80 $ $ |C \cup M| = 260 - 80 $ $ |C \cup M| = 180 $Conclusion
Therefore, 180 students like at least one of the drinks (cold drinks or milkshakes).
Important Questions from Set Theory and Venn Diagram (Notes)
Match List-I with List-II
List-1 List-II (A) If X and Y are two sets such that n(X)= 17, n(Y)=23, n(X $\cup$ Y)=38, then n(X $\cap$ Y) is (I) 20 (B)) If n(X) = 28,n(Y) = 32,n(X$\cap$Y) = 10, then n(X$\cup$Y) is (II) 10 (C) If n(X) = 10, then n(7X) is (III) 50 (D) If n(Y) = 20, then n($\frac{Y}{2}$) is (IV) 2 Choose the Correct answer from the options given below:
- From the given sets, which is an infinite set:
1. {x: x $\in$ N and (x-1)(x-2) = 0}
2. {x: x $\in$ N and x is prime number and less than 199}
3. {x: x $\in$ N and x$^5$ - 1 = 0}
4. {x: x $\in$ N and x is odd} Consider the following relation R={(4,5),(5,4), (7,6),(6,7)} on set I={4,5,6,7}. Which of the following properties relation R does not have?
A. Reflexive property
B. Symmetric property
C. Transitive property
D. Antisymmetric property
Choose the correct answer from the options given below:Find the least upper bound and greatest lower bound of $S=\{X,Y,Z\}$ if they exist, of the poset whose Hasse diagram is shown below:
- In a class, 40 like Math, 35 like Science, 30 like English; 15 like both Math and Science, 12 like Math and English, 10 like Science and English, 5 like all three. How many like atleast one?
