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Q1. List all the elements of the following setC = {x : x is a month of the year having 31 days starting with J}

Solution

There are three months starting with J: January, June and July. June has 30 days in it. So C = {January, July}
Q2. Is the collection of all intelligent persons in India a set?

Solution

The collection of all intelligent persons in India is not well- defined, because the criterion for determining an intelligent person may vary. Hence, the given collection is not a set.
Q3. In a pollution study of 1500 Indian rivers the following data were reported. 520 were polluted by sulphur compunds, 335 were polluted by phosphorous, 425 were polluted by crude oil, 100 were polluted by both crude oil and sulphur compunds, 152 were polluted by sulphate and phosphate compounds only, 150 were polluted by phosphate and crude oil, and 28 were polluted by all 3 compounds. How many of the rivers were polluted by exactly one of the 3 impurities?

Solution

S=river polluted by sulphur             n(S)=520 P=river polluted by phosphorous     n(P)=335 C=river polluted by crude oil            n(C)=425 n(CintersectionS)=100 n(PintersectionS)=152 n(PintersectionC)=150 n(PintersectionSintersectionC )=3 rivers polluted by  sulphur only =n(S)-n(PintersectionS)-n(SintersectionC)+n(PintersectionCintersectionS)                                            =520-152-100+3=271 rivers polluted by  phosphorous only =n(P)-n(PintersectionS)-n(PintersectionC)+n(PintersectionCintersectionS)                                               =335-152-150+3=36 rivers polluted by crude oil only=n(C)-n(SintersectionC)-n(PintersectionC)+n(PintersectionCintersectionS)                                             =425-100-150+3=178 so the required no of rivers=271+178+36=485
Q4. Given the set A = {a, c, e}, B = {b, d, f} and C = {b, d, f, h}. Can we consider the set X = {a, b, c, d, e, f , g, h} as universal set for all the three sets A, B, C?

Solution

Yes, because the sets A, B, C are subsets of X.
Q5. If A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, write a subset B of A that contain all multiples of 3.

Solution

B = {3, 6, 9}
Q6. If  A = {2, 4, 6, 8}, B = {3, 6, 9, 12}, then find A – (B – A).

Solution

B – A = {3, 9, 12} A – (B – A) = {2, 4, 6, 8}
Q7. Is the collection of all even numbers between 7 and 19 a set?

Solution

Given collection is a set as it is well-defined and it contains the elements 8, 10, 12, 14, 16 and 18.
Q8. Are A = {x : x – 5 = 0} and B = {x : x is a positive  integral root of the equation x2 - 2x - 15} equal sets?

Solution

G i v e n space t h a t space A equals open curly brackets x colon x minus 5 equals 0 close curly brackets T h u s comma space A equals open curly brackets 5 close curly brackets C o n s i d e r space t h e space s e t space B equals open curly brackets x colon x space i s space a space p o s i t i v e space space i n t e g r a l space r o o t space o f space t h e space e q u a t i o n space x squared minus 2 x minus 15 close curly brackets F a c t o r i z i n g space t h e space g i v e n space e q u a t i o n comma space w e space h a v e comma x squared minus 2 x minus 15 equals 0 rightwards double arrow x squared minus 5 x plus 3 x minus 15 equals 0 rightwards double arrow x open parentheses x minus 5 close parentheses plus 3 open parentheses x minus 5 close parentheses equals 0 rightwards double arrow open parentheses x plus 3 close parentheses open parentheses x minus 5 close parentheses equals 0 rightwards double arrow x equals negative 3 space o r space x equals 5 S i n c e space x equals negative 3 space i s space n o t space a space p o s i t i v e space i n t e g r a l space r o o t comma space w e space h a v e comma space B equals open curly brackets 5 close curly brackets T h u s comma space A equals B
Q9. Write the set {x : x is a month of a year not having 30 days} in roster form:

Solution

{January, February, March, May, July, August, October, December}
Q10. Is the set of integers finite or infinite?

Solution

The set of integers is an infinite set as there are infinite number of integers.


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