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Exercise 2.1

1. Express the following sets in tabular method :

(a) {xN:x^2! 9 and x^3  130 }

(b) {xZ:x^2! 5 and x^3 d 36 }
(c) {xN:x, factors of 36 and multiple of 6}.

(d) {xN:x^3  25 and x^4  264 }

2. Express the following sets in set builder method :

(a) { 3 , 5 , 7 , 9 , 11 } (b) { 1 , 2 , 3 , 4 , 6 , 9 , 12 , 18 , 36 }
(c) { 4 , 8 ,12, 16 , 20 , 24 , 28 , 32 , 36 , 40 } (d) {r 4 ,r 5 ,r 6 }

3. If A { 2 , 3 , 4 },B { 1 , 2 ,a} and C { 2 ,a,b}, determine the sets given below:

(a) B\C (b) A‰B (c) AˆC (d) A‰(BˆC) (e) Aˆ(B‰C)

4. If U { 1 , 2 , 3 , 4 , 5 , 6 , 7 }, A { 1 , 3 , 5 }, B { 2 , 4 , 6 } and C { 3 , 4 , 5 , 6 , 7 }, justify
   the followings :
   (i) (A‰B)c AcˆBc^ (ii) (BˆC)c Bc‰Cc
   (iii) (A‰B)ˆC (AˆC)‰(BˆC) (iv)
   (AˆB)‰C (A‰C)ˆ(B‰C)


5. If Q {x,y} and R {m,n,l}, find P(Q) and P(R).


6. If A {a,b},B {a,b,c} and C A‰B, show that the number of elements of
   P(C) is 2 n, where n is the number of element of C.


7. (a) If (x 1 ,y 2 ) (y 2 , 2 x 1 ), find the value of x and y.
   (b) If (axcy,a^2 c^2 ) ( 0 ,aycx), find the value of (x,y).

(c) If ( 6 xy, 13 ) ( 1 , 3 x 2 y), find the value of (x,y).

8. (a) If P {a},Q {b,c} then, find PuQ and QuP.

(b) If A { 3 , 4 , 5 },B { 4 , 5 , 6 } and C {x,y}, find (AˆB)uC.
(c) If P { 3 , 5 , 7 },Q { 5 , 7 } and R P\Q, find (P‰Q)uR.

9. If A and B are the sets of all factors of 35 and 45 respectively, find A‰B
   andAˆB.


10. Find the set of the number where 31 is the remainder in each case when 346 and
    556 are divided by natural numbers.


11. Out of 30 students of any class, 20 students like football and 15 students like
    cricket. The number of students who like any one of the two is 10. Show with the
    help of Venn diagram, the number of students who do not like two of the sports.


12. Out of 100 students in any exam, 65% in Bangla, 48% in both Bangla and
    English have passed and 15% have failed in both subjects.