Question 1:Decide, among the following sets, which sets are subsets of one and another: A = { x : x Î R and x satisfy x2 – 8x + 12 = 0 }, B = { 2, 4, 6 }, C = { 2, 4, 6, 8, . . . }, D = { 6 }.
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Question 2:In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example. (i) If x Î A and A Î B , then x Î B (ii) If A Ì B and B Î C , then A Î C (iii) If A Ì B and B Ì C , then A Ì C (iv) If A Ë B and B Ë C , then A Ë C (v) If x Î A and A Ë B , then x Î B (vi) If A Ì B and x Ï B , then x Ï A
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Question 3:Let A, B, and C be the sets such that A È B = A È C and A Ç B = A Ç C. Show that B = C.
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Question 4:Show that the following four conditions are equivalent : (i) A Ì B(ii) A – B = f (iii) A È B = B (iv) A Ç B = A
Question 5:Show that if A Ì B, then C – B Ì C – A.
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Question 6:Assume that P ( A ) = P ( B ). Show that A = B
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Question 7:Is it true that for any sets A and B, P ( A ) È P ( B ) = P ( A È B )? Justify your answer.
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Question 8:Show that for any sets A and B, A = ( A Ç B ) È ( A – B ) and A È ( B – A ) = ( A È B )
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Question 9:Using properties of sets, show that (i) A È ( A Ç B ) = A (ii) A Ç ( A È B ) = A.
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Question 10:Show that A Ç B = A Ç C need not imply B = C.
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Question 11:Let A and B be sets. If A Ç X = B Ç X = f and A È X = B È X for some set X, show that A = B. (Hints A = A Ç ( A È X ) , B = B Ç ( B È X ) and use Distributive law )
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Question 12:Find sets A, B and C such that A Ç B, B Ç C and A Ç C are non-empty sets and A Ç B Ç C = f.
Question 13:In a survey of 600 students in a school, 150 students were found to be taking tea and 225 taking coffee, 100 were taking both tea and coffee. Find how many students were taking neither tea nor coffee?
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Question 14:In a group of students, 100 students know Hindi, 50 know English and 25 know both. Each of the students knows either Hindi or English. How many students are there in the group?
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Question 15:In a survey of 60 people, it was found that 25 people read newspaper H, 26 read newspaper T, 26 read newspaper I, 9 read both H and I, 11 read both H and T, 8 read both T and I, 3 read all three newspapers. Find: (i) the number of people who read at least one of the newspapers. (ii) the number of people who read exactly one newspaper.
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Question 16:In a survey it was found that 21 people liked product A, 26 liked product B and 29 liked product C. If 14 people liked products A and B, 12 people liked products C and A, 14 people liked products B and C and 8 liked all the three products. Find how many liked product C only.
