NCERT Class 11-Math's Exemplar Chapter 1 Sets CBSE Board Problems

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Long Answer Type

Question 10:

For all sets A, B and C

Is ?

Justify your answer.

Answer:

Yes

Let

So

Now, conversely

Let

So

From

Question 11:

Let A, B and C be sets. Then show that

Answer:

We first show that

Let . Then

Thus,

Now we will show that

Let

Thus,

So, from (1) and (2), we have

Question 12:

Let P be the set of prime numbers and let . Prove that S ⊂ P.

Answer:

Now the equivalent contrapositive statement of .

Let

is a composite number

Let us now assume that

Which is not true for all composite number, say for because which can not be equal to the sum of any prime number m and 1.

Thus, we arrive at a contradiction

Thus, when we arrive at

So

Question 13:

From 50 students taking examinations in Mathematics, Physics and Chemistry, each of the student has passed in at least one of the subject, 37 passed Mathematics, 24 Physics and 43 Chemistry. At most 19 passed Mathematics and Physics, at most 29 Mathematics and Chemistry and at most 20 Physics and Chemistry. What is the largest possible number that could have passed all three examination?

Answer:

Let be the set of students passing in Mathematics

P be the set of students passing in Physics

C be the set of students passing in Chemistry

Now,

Thus, the largest possible number that could have passed all the three examinations is 14.

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