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Q9. If A = {3, 6, 9, 12, 15, 18, 21}, B = { 4, 8, 12, 16, 20 }, C = { 2, 4, 6, 8, 10, 12, 14, 16 }, D = {5, 10, 15, 20 }; find

(i) A – B         (ii) A – C          (iii) A – D        (iv) B – A            (v) C – A           (vi) D – A

(vii) B – C       (viii) B – D       (ix) C – B       (x) D – B            (xi) C – D            (xii) D – C

Q10. If X= { a, b, c, d } and Y = { f, b, d, g}, find

(i) X – Y

(ii) Y – X

(iii) X \cap Y

Q11. If R is the set of real numbers and Q is the set of rational numbers, then what is R – Q?

Q12. State whether each of the following statement is true or false. Justify your answer.

(i) { 2, 3, 4, 5 } and { 3, 6} are disjoint sets.

Q12. State whether each of the following statement is true or false. Justify your answer.

(ii) { a, e, i, o, u } and { a, b, c, d }are disjoint sets

Q12. State whether each of the following statement is true or false. Justify your answer.

(iii) { 2, 6, 10, 14 } and { 3, 7, 11, 15} are disjoint sets.

Q12. State whether each of the following statement is true or false. Justify your answer.

(iv) { 2, 6, 10 } and { 3, 7, 11} are disjoint sets.

Q1. If X and Y are two sets such that n ( X ) = 17, n ( Y ) = 23 and n ( X \cup Y ) = 38, find n ( X \cap Y ).

Q2. If X and Y are two sets such that X \cup Y has 18 elements, X has 8 elements and Y has 15 elements ; how many elements does X \cap Y have?

Q3. In a group of 400 people, 250 can speak Hindi and 200 can speak English. How many people can speak both Hindi and English?

Q4. If S and T are two sets such that S has 21 elements, T has 32 elements, and S \cap T has 11 elements, how many elements does S \cup T have?

Q5. If X and Y are two sets such that X has 40 elements, X \cup Y has 60 elements and X \cap  Y has 10 elements, how many elements does Y have?

Q6. In a group of 70 people, 37 like coffee, 52 like tea and each person likes at least one of the two drinks. How many people like both coffee and tea?

Q7. In a group of 65 people, 40 like cricket, 10 like both cricket and tennis. How many like tennis only and not cricket? How many like tennis?

Q8. In a committee, 50 people speak French, 20 speak Spanish and 10 speak both Spanish and French. How many speak at least one of these two languages?

Q1. Decide, among the following sets, which sets are subsets of one and another:

A = { x : x \in R and x satisfy x^{2} – 8x + 12 = 0 }, B = { 2, 4, 6 },

C = { 2, 4, 6, 8, . . . }, D = { 6 }.

Q2. 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 \in A and A \in B , then x \in B

Q2. 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.

(ii) If A \subset B and B \in C , then A \in C

Q2. 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.

(iii) If A \subset B and B \subset C , then A \subsetC

Q2. 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.

(iv) If A \not\subset B and B \not\subset C , then A \not\subset C

Q2. 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.

(v) If x \in A and A \not\subset B , then x \in B

Q2. 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.

(vi) If A \subset B and x \notin B , then x \notin A

Q3. Let A, B, and C be the sets such that A \cup B = A \cup C and A \cap B = A \cap C. Show that B = C.

       

Q4. Show that the following four conditions are equivalent :

(i) A \subset B(ii) A – B = \phi (iii) A \cup B = B (iv) A \cap B = A

 

Q5. Show that if A \subsetB, then C – B \subset C – A.

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