Analyzing the Survey Data
The goal is to find the number of people who like neither tea nor coffee from the given survey results.
Given Survey Information
- Total surveyed: 100
- Likes Tea (|T|): 60
- Likes Coffee (|C|): 50
- Likes Both Tea and Coffee (|T ∩ C|): 25
Calculating Union of Preferences
First, determine the number of people who like at least one beverage (Tea or Coffee or Both). This is calculated using the Principle of Inclusion-Exclusion:
$|T \cup C| = |T| + |C| - |T \cap C|$
Substituting the values:
$|T \cup C| = 60 + 50 - 25$
$|T \cup C| = 110 - 25$
$|T \cup C| = 85$
So, 85 people like tea, coffee, or both.
Determining Those Who Like Neither
To find the number of people who like neither drink, subtract the count of those who like at least one drink from the total number of people surveyed:
Number liking Neither = Total People - $|T \cup C|$
Calculation:
$100 - 85 = 15$
Therefore, 15 people like neither tea nor coffee.
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?
