Set Theory

Study Material (PDF)
Self Assesment
Study Material (PDF)
Self Assesment

Click on each question to see answer & solution.

Question No: #41

For any two set `A` & `B`, prove that -

(a) `A\cap(B-A)=\phi`
(b) `A\cup(B-A)=A\cupB`
(c) If `A\cupB=A\capB` then prove that `A=B`
(d) If `A\capB^c=\phi` and `A^c\capB=\phi` then show that `A=B`
(e) `A-B=A-(A\capB)`
Ans: N.A.
SEE SOLUTION

Question No: #42

For any two sets `A` & `B`, prove that -

(a) `A\subseteq A\cupB` and `B\subseteq A\cupB`
(b) `A\capB \subseteq A` and `A\capB \subseteq B`
Ans: N.A.
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Question No: #43

For any two sets `A` & `B`, if `A\subseteqB`, then show that `A\cupB=B` and `A\capB=A`
Ans: N.A.
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Question No: #44

For any three sets `A,B,C` -

(a) if `A\subseteqC` and `B\subseteqC`, then show that `A\cupB\subseteqC`
(b) if `C\subseteqA` and `C\subseteqB`, then show that `C\subseteq A\capB`
Ans: N.A.
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Question No: #45

For any three sets `A,B,C`, prove that -

(a) `A\cap(B-C)=(A\capB)-(A\capC)`
(b) `(A\cupB)-C=(A-C)\cup(B-C)`
(c) `(A\capB)-C=(A-C)\cap(B-C)`
(d) `A-(B\cupC)=(A-B)\cap(A-C)`
(e) `A-(B\capC)=(A-B)\cup(A-C)`
(f) `A-(B-C)=(A-B)\cup(A\capC)`
Ans: N.A.
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Question No: #46

If `A = {1,2,3,4,5}` and `B \cup C = {3,4, 6}`, then find `(A-B) \cap (A-C)`.
Ans: `{1,2,5}`
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Question No: #47

For any three sets `A,B,C`, if `A\capC=B\capC=\phi` and `A\cupC=B\cupC`, then prove that `A=B`
Ans: N.A,
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Question No: #48

For any three sets `A,B,C`, if `A\capC=B\capC=\phi` and `A\capC^c=B\capC^c`, then prove that `A=B`
Ans: N.A.
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Question No: #49

For any three sets `A,B,C`, if `A\capB=A\capC` and `A\cupB=A\cupC`, then prove that `B=C`
Ans: N.A.
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Question No: #50

Three daily newspapers X, Y, Z are published in a city. 65% of the people in the city read X magazine, 54% Y magazine and 45% Z magazine. 38% of people read X and Y; 32% of people read Y and Z; 28% read X and Z magazines and 12% do not read any of these three types of magazines. If the total population of the city is 1000000, determine how many people in the city read all three magazines.
Ans: 220000
SEE SOLUTION