Understand the Mathematics of Set theory. Click on the link to Watch the VIDEO explanation: Watch Video
Numerical
Problem: In a class of 60 boys, there are 45 boys who play cards and 30 boys who play carrom. Using set theory, find the following:
1. How many boys play both games?
2. How many boys play card only?
3. How many boys play carrom only?
Solution: Let, A is equal to Set of boys who play cards
B is equal to Set of boys who play carrom
Set A and set B are shown by the hatched ovals in the fig.. Drag them and placed them on the background shown. Click on the OK button.
A minus B, A intersection B and B minus A are shown by the hatched portion in the boxes. Click on the next button.
Therefore, A union B is equal to Set of boys who play cards or carrom or both
A intersection B is equal to Set of boys who play cards and carrom both
A minus B is equal to Set of boys who play cards only
B minus A is equal to Set of boys who play carrom only
Click on the next button
By the given data: n of A union B is equal to 60, n of A equals 45 and n of B equals 30
We know that n of A union B is equal to n of A plus n of B minus n of A intersection B
Now, key in the values for n of A union B, n of A and n of B in the respective boxes and calculate the values of A intersection B. Click on the OK button to check your answer.
We also know that n of A is equal to n of A minus B plus n of A intersection B. key in the values for n of A and n of A intersection B. Find the values of n of A minus B and click on the OK button.
Similarly, Find the values of n of B minus A and check your answer. Click on the next button.
Therefore, Number of boys who play both games is equal to 15.
Number of boys who play cards only is equal to 30
Number of boys who play carrom only is equal to 15
Numerical
Problem: In a class of 60 boys, there are 45 boys who play cards and 30 boys who play carrom. Using set theory, find the following:
1. How many boys play both games?
2. How many boys play card only?
3. How many boys play carrom only?
Solution: Let, A is equal to Set of boys who play cards
B is equal to Set of boys who play carrom
Set A and set B are shown by the hatched ovals in the fig.. Drag them and placed them on the background shown. Click on the OK button.
A minus B, A intersection B and B minus A are shown by the hatched portion in the boxes. Click on the next button.
Therefore, A union B is equal to Set of boys who play cards or carrom or both
A intersection B is equal to Set of boys who play cards and carrom both
A minus B is equal to Set of boys who play cards only
B minus A is equal to Set of boys who play carrom only
Click on the next button
By the given data: n of A union B is equal to 60, n of A equals 45 and n of B equals 30
We know that n of A union B is equal to n of A plus n of B minus n of A intersection B
Now, key in the values for n of A union B, n of A and n of B in the respective boxes and calculate the values of A intersection B. Click on the OK button to check your answer.
We also know that n of A is equal to n of A minus B plus n of A intersection B. key in the values for n of A and n of A intersection B. Find the values of n of A minus B and click on the OK button.
Similarly, Find the values of n of B minus A and check your answer. Click on the next button.
Therefore, Number of boys who play both games is equal to 15.
Number of boys who play cards only is equal to 30
Number of boys who play carrom only is equal to 15
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