Question 1: If and are two sets such that and , find .

Answer:

Given

We know:

Question 2: If and are two sets such that has elements, has elements and has elements, how many elements does have?

Answer:

Given:

We know:

Question 3: In a school there are teachers who teach mathematics or physics. Of these, teach mathematics and teach physics and mathematics. How many teach physics?

Answer:

Given:

We know:

Question 4: In a group of people, like coffee, like tea and each person likes at east one of the two drinks. How many like both coffee and tea?

Answer:

Given:

We know:

Question 5: Let and be two sets such that: and . Find : (i) (ii) (iii)

Answer:

Given:

i)

ii)

iii)

Question 6: A survey shows that of the Indians like oranges, whereas like bananas. What percentage of the Indians like both oranges and bananas?

Answer:

Let the population be

Therefore

Also

We know:

Therefore of population likes both Banana and Oranges.

Question 7: In a group of persons, can speak Hindi and can speak English. Find: (i) how many can speak both Hindi and English (ii) how many can speak Hindi only (iii) how many can speak English only

Answer:

Given:

i) We know:

Therefore people can speak both Hindi and English

ii)

Therefore people can speak Hindi only

iii)

Therefore people speak English only.

Question 8: In a group of persons, drink tea but not coffee and drink tea. Find: (i) how many drink tea and coffee both (ii) how many drink coffee but not tea.

Answer:

Given:

i)

Therefore people drink both Tea and Coffee.

ii)

Now we need to find

Question 9: In a survey of people, it was found that people read newspaper read newspaper read newspaper read both and read both and read both and read all three newspapers. Find: (i) the numbers of people who read at least one of the newspapers. (ii) the number of people who read exactly one newspaper.

Answer:

Given:

i)

Note: There are 8 people who do no read any news paper. We should not assume that all read newspaper.

ii)

You can also do it by looking at the venn diagram. Venn diagram is more intutitive.

Question 10: Of the members of three athletic teams in a certain school, are in the basketball team, in hockey team and in the football team. play hockey and basket ball, play hockey and football, play football and basketball and play all the three games. How many members are there in all?

Answer:

Given:

We know:

Therefore total number of members in all the teams are

Question 11: In a group of people, there are who can speak Hindi and who can speak Bengali. How many can speak Hindi only? How many can speak Bengali ? How many can speak both Hindi and Bengali?

Answer:

Given:

We know:

Therefore the number of people who can speak both Hindi and Bengali is .

Number of people who can speak only Hindi

No of people who only speak Bengali

Question 12: A survey of television viewers produced the following in-formation; watch football, watch hockey, watch basketball, watch football and basketball, watch football and hockey, watch hockey and basketball, do not watch any of the three games. How many watch all the three games? How many watch exactly one of the three games?

Answer:

Given:

Now, the number of students who watch all the games

No of students who watch exactly one game

Question 13: In a survey of persons it was found that read magazine read magazine read magazine read magazines and read magazines and read magazines and and read all the three magazines. Find: (i) How many read none of three magazines? (ii) How many read magazine C only?

Answer:

Given:

i) Number of people who read none of the three magazines

ii) Number of students who read only

Question 14: In a survey of students, the number of students studying the various languages were found to be: English only , English but not Hindi , English and Sanskrit , English , Sanskrit , Sanskrit and Hindi , no language . Find:

(i) How many students were studying Hindi?

(ii) How many students were studying English and Hindi?

Answer:

Given:

ii)

i)

Therefore number of students studying Hindi

Question 15: In a survey it was found that persons liked product liked product and liked product . If persons liked products and persons liked product and persons liked products and and liked all the three products. Find how many liked product only.

Answer:

Given:

Number of people liking Product only

Therefore number of people liking is

Question 16: A market research group conducted survey on persons and reported that persons liked product and persons liked product . What is the least number of persons that must have liked both products?

Answer:

Given:

We know: