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****** SETS ******
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*Set:Collections of well-defined objects is called Set. *Elements of set:The objects of a set are called its member or elements *Finite set: The set having fixed number of elements is called finite set. *Infinite set: The set having uncountable no of elements icalled infite set. *Null or empty set: The sets having no elements is called null set or empty set. *Cardinal number of set: The number of elements in a set is called cardinal number of sets. |
Sets are represented in two different ways:Roaster method/tabularform and Set-builder Form/Rule method. *Roaster method:In this method ,the elements of the sets presented or written directly. *Set builder form: In this method inspite of showing the elements,description of the elements are shown. With following eg. are it can be explained in better way. Roaster form: {8,10,12,14,16,18} Set-builder form : {x|x=2*n,nEN,4<=n<=9} Roaster form: {16,25,36,49,81,100} Set-builder form:{x|x=n*n,nEN,4<=n<=10} Roaster form:{5,6} Set-builder form:{x|x is a factor of equation x*x+11*x+30} |
| Q:Show the following Roaster form set into Set builder form a){1,2,3,5,7,11,13,17,19,23,29} b){9,36,81,144,225} c){1,2,3,5} Ans: a){x|x is prime number, 1<=x<=30} b){x| x is square of multiples of 3,1<=x<=5} c){x|x is first four prime natural numbers.} check the answer!!!
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Q:Show the following Set builder form set into Roaster form a){x|xEN,x is prime factors of 216} b){x|x E months of 30 days.} c){x|x is factors of 72.} Ans:a) {1,2,3}
b){April,june,September,November} c){2,3,4,6,8,9,12,24,36,72} check the answer!!!
| Q:Check whether the following pair of sets are equal , equivalent or not ? a) A = {x|x is vowel},B ={1,2,3,4,5} b) A= {x|x = 3*n,xEN,n<=5},B= {3,6,9,12,15} c) A= {x|x = 2*n,xEN,n<=3}, B = {1,2,3,4,} Ans:a)n(A)=5,n(B)=5 ,b)n(A)=5,n(B)=5 c)n(A)=3,n(B)=4 check the answer!!! |
Q:Check whether set A is subset of set B or not a)A= {1,2,3,4,5} B={2,3,4,5,1,8,9} b)A= {2,3,4,5} B= {1,3,5,7,9,11,13} c)A= {x|x = n*n,xEN,n<=10} B={x|x is first hundred natural numbers.} Ans: check the answer!!! |
| Q: A={9,36,81,144,225} B= {x|x = 3*n,xEN,n<=5} Find a) A U B b)A U (A U B) c) A intersection B d)A intersection(A intersection B) Ans: a) A U B = {3,6,9,12,15,36,81,144,225}
b)A U (A U B) ={3,6,9,12,15,36,81,144,225} c)A intersection B ={9} d)A intersection(A intersection B) = {9} check the answer!!! |
Q: A = {8,9,10,11} B = {1,2,3,4,5,9,11,13} a) A-B b) Give one example of disjoint sets. c) give two examples of infinite sets. Ans:a) {9,11}
b) Disjoint set: A = {1,2,3,4,5} B= {9,11,13} c) two examples of infinite sets: A={x|x=3n-1,n>0},B={x|x is star in the universe} check the answer!!! |
**** TRY BY YOURSELF****
Q:1 State which of the following is finite set and infinite set.
a){x|x is star in the universe}
b) {x|x=n/2,n<0}
c) {1,2,3,4,5}
d){9,11,13}
e)a){x|x is letter in elephant}
Q:2 State which of the following is finite,singleton and empty set.
a){x|x is vowel in intermission}
b){x|x is consonant in egg}
c){x|x is vowel in sitting}
d){x|x is positive multiple of 10,x<10}
e){x|x is multiple of 2,x= 2*n+1,nEN}
Q:3 Write the following sets into set builder form
a) {1,3,5,7,9}
b) {17,34,51,68,95}
c) {a,e,i,o,u}
d) {January,june,july}
e) {lake,pond,ocean,river,sea}
Q:4 Write the following sets into Roaster form
a) {x|x is Metro city of India}
b){x|x is factor of 144}
c){x|x is planet in solar system}
d){x|x =2*n+3,1<=n<=6}
e){x|x is frst five multiples of 23}
Q:5 A={2,3,9,12,13} B= {23,9,12,13,16} C= {3,4,5,89,11}
a)AU(BUC)
b)BU(AUC)
c)CU(AUB)
d)(A intersection)U C
e)A intersection (BUC)
1.Ans:a)infinite set b)infinite set c)finite set d) finite set
2.Ans:a) finite set b)singleton set c)singleton set d)empty set e)empty set