Analyzing Survey Data for City Visits
We are given data from a survey of 1000 people about their visits to Delhi and Mumbai.
- Total people surveyed: 1000
- Visited Delhi (D): 600
- Visited Mumbai (M): 450
- Visited Both Delhi and Mumbai (D $\cap$ M): 250
Calculating Visitors of Only One City
To find the number of people who visited only Delhi, we subtract those who visited both cities from the total who visited Delhi.
People who visited only Delhi = Number who visited Delhi - Number who visited both
Only Delhi = $600 - 250 = 350$
Similarly, to find the number of people who visited only Mumbai, we subtract those who visited both cities from the total who visited Mumbai.
People who visited only Mumbai = Number who visited Mumbai - Number who visited both
Only Mumbai = $450 - 250 = 200$
Determining the Ratio
The question asks for the ratio of people who visited only Delhi to those who visited only Mumbai.
Ratio = (Number who visited only Delhi) : (Number who visited only Mumbai)
Ratio = $350 : 200$
To simplify the ratio, we find the greatest common divisor (GCD) of 350 and 200, which is 50.
Simplified Ratio = $\frac{350 \div 50}{200 \div 50} = \frac{7}{4}$
Therefore, the ratio is 7 : 4.
This corresponds to Option 4.
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?
