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