Bissoy.com
Doctors Medicines MCQs Q&A

If X and Y are two sets, such that X ∪ Y has 400 elements, X has 280 elements and Y has 220 elements, how many elements does X ∩ Y have?

If X and Y are two sets, such that X ∪ Y has 400 elements, X has 280 elements and Y has 220 elements, how many elements does X ∩ Y have? Correct Answer 100

Concept:

n(A ⋃ B) = n(A) + n(B) - n(A ⋂ B)

Calculation:

Here, n(X ∪ Y) = 400, n(X) = 280, n(Y) = 220

n(X ⋃ Y) = n(X) + n(Y) – n(X ⋂ Y)

⇒ n(X ∩ Y) =  - n(X ⋃ Y) 

= (280 + 220) - 400

= 100

Hence, option (3) is correct.

Related Questions

Consider the following statements in respect of sets: 1. The union over the intersection of sets is distributive. 2. The complement of the union of two sets is equal to the intersection of their complements. 3. If the difference between the two sets is equal to the empty set, then the two sets must be equal. Which of the above statements are correct?
Radon 222 এবং Radon-220 উভয়ই Radon এর আইসোটোপ। যদি Radon-222 এর নিউক্লিয়াসে 136 টি নিউট্রন থাকে তাহলে Radon-220 এর নিউক্লিয়াসে কতগুলো প্রোটন থাকবে? ( Radon-222 and Radon-220 are the isotopes of Radon. If Radon-222 has 136 neutrons then what will be the number of protons in the nucleus of Radon-220?)
The sale of different commodities in a shop in various years is given in the table. In which year did the total number of refrigerators and washing machines sold exceed the number of TVs sold by 100? Year TV Washing Machine Refrigerator AC 1996 320 200 220 1500 1997 350 220 190 1700 1998 315 250 200 1800 1999 400 280 150 2000
A manufacturer of TV wants to make a profit of Tk. 300,000 on sale of 200 TV sets. It costs Tk. 10,000 each to make the first 100 TV sets and Tk. 7,500 each to make TV sets after the first 100 sets. What should be the selling price of each TV sets in Taka?
Study the following table carefully to answer the given question. Number of employees in different departments of five organisations Organisation →  Department ↓  A B C D E HR 145 80 120 180 160 Finance 120 75 100 220 140 Marketing 150 90 115 200 190 IT 225 110 160 280 220 Administration 180 120 130 110 130 What is the ratio between the number of employees from Finance and Marketing departments together of organization B and these two departments together of organisation D respectively?
If X and Y are two sets such that X ∪ Y has 70 elements, X has 38 elements and Y has 42 elements, how many elements does X ∩ Y have? 
If X and Y are two sets, such that X ∪ Y has 40 elements, X has 28 elements and Y has 22 elements, how many elements does X ∩ Y have ?
If X and Y are two sets, such that X ∪ Y has 40 elements, X has 28 elements and Y has 22 elements, how many elements does X ∩ Y have?
Study the following table and answer the question: Number of student Appeared (A) and Passed (P) in an annual examination from schools Q, R, S & T in five years (2014 to 2018)   Year Schools Q R S T A P A P A P A P 2014 320 240 400 340 420 273 250 225 2015 400 320 380 285 350 280 300 228 2016 440 286 360 288 330 264 320 256 2017 350 252 420 294 380 247 350 315 2018 375 320 450 405 400 344 375 300 The total number of students passed from school Q in 2014 and 2018 is what percent less than the total number of students appeared from school R and S in 2017?
Study the following table and answer the question: Number of students Appeared (A) and Passed (P) in an annual examination from four schools Q, R. S & T in five years (2014 to 2018)   Year Schools Q R S T A P A P A P A P 2014 320 240 400 340 420 273 250 225 2015 400 320 380 285 350 280 300 228 2016 440 286 360 288 330 264 320 256 2017 350 252 420 294 380 247 350 315 2018 375 320 450 405 400 344 375 300 The total number of students passed from school S in 2014 and 2017 is what percent of 90% of the total number of students appeared from school T in 2015, 2016 and 2017? (correct to one decimal place)