Question

Write the following sets in Roster form: (i) The set of letters in the word 'MEERUT' (ii) The set of letters in the word 'UNIVERSAL' (iii) $A=\{x:x=y+3,y\in Nandy>3\}$ (iv)$B=\{p:p\in Wand{p}^2<20\}$ (v) $C=\{x:x\text{is composite number and~}5\le x\le 21\}$

Answer 1

(i) $\text{Roster form of the set of letters in the word "MEERUT"}=\{m,e,r,u,t\}Ans.$ (ii) $\text{Roster form of the set of letters in the word "UNIVERSAL"}=\{u,n,i,v,e,r,s,a,l\}Ans.$ (iii) $A=\{x:x=y+3,y\in Nandy>3\}x=y+3Wheny=4,x=4+3=7Wheny=5,x=5+3=8Wheny=6,x=6+3=9Wheny=7,x=7+3=10Wheny=8,x=8+3=11......................................................................................................\therefore RosterformofthegivensetA=\{7,8,9,10,11\}Ans.$ (iv)$B=\{P:P\in Wand{P}^2<20\}When{P}^2=0P=\sqrt{0}=0When{P}^2=1P=\sqrt{1}=1When{P}^2=4P=\sqrt{4}=2When{P}^2=9P=\sqrt{9}=3When{P}^2=16P=\sqrt{16}=4\therefore \text{Roster form of the given set B = 0,1,2,3,4}$ (v) $C=\{x:xiscompositenumberand5\le x\le 21\}meansx=5,6,7,8,9,\mathrm{10............21}\text{But we are given that x is a composite number}\therefore x=6,8,9,10,12,14,15,16,18,20,21\therefore \text{Roster form of the given set C = 6,8,9,10,12,14,15,16,18,20,21}Ans.\text{Note: Composite numbers : The natural numbers (greater than 1), which are not prime, are called composite numbers.}$