Question -
Answer -
(i)┬а{x: x is a letter before e in the English alphabet}
So, when we read whole sentence it becomes x is such that x is a letterbefore тАШeтАЩ in the English alphabet. Now letters before тАШeтАЩ are a,b,c,d.
тИ┤┬аRosterform will be {a,b,c,d}.
(ii)┬а{x┬атИИN: x2┬а< 25}
x┬атИИ┬аN that implies x is a natural number.
x2┬а< 25
x <┬а┬▒5
As x belongs to the natural number that means x < 5.
All numbers less than 5 are 1,2,3,4.
тИ┤┬аRosterform will be {1,2,3,4}.
(iii)┬а{xтИИ┬аN:x is a prime number, 10 < x < 20}
X is a natural number and is between 10 and 20.
X is such that X is a prime number between 10 and 20.
Prime numbers between 10 and 20 are 11,13,17,19.
тИ┤┬аRosterform will be {11,13,17,19}.
(iv)┬а{xтИИ┬аN:x = 2n, n тИИ┬аN}
X is a natural number also x = 2n
тИ┤┬аRosterform will be {2,4,6,8тАж..}.
This an infinite set.
(v)┬а{xтИИ┬аR:x > x}
Any real number is equal to its value it is neither less nor greater.
So, Roster form of such real numbers which has value less than itself hasno such numbers.
тИ┤┬аRosterform will be┬а╧Х. This is called a null set.
(vi)┬а{x: x is a prime number which is a divisor of 60}
All numbers which are divisor of 60 are = 1,2,3,4,5,6,10,12,15,20,30,60.
Now, prime numbers are = 2, 3, 5.
тИ┤┬аRosterform will be {2, 3, 5}.
(vii)┬а{x: x is a two digit number such that the sum of its digits is 8}
Numbers which have sum of its digits as 8 are = 17, 26, 35, 44, 53, 62,71, 80
тИ┤Roster form will be {17, 26, 35, 44, 53, 62, 71, 80}.
(viii)The set of all letters in the word тАШTrigonometryтАЩ
As repetition is not allowed in a set, then the distinct letters are
Trigonometry = t, r, i, g, o, n, m, e, y
тИ┤┬аRosterform will be {t, r, i, g, o, n, m, e, y}
(ix)The set of all letters in the word тАШBetter.тАЩ
As repetition is not allowed in a set, then the distinct letters are
Better = b, e, t, r
тИ┤┬аRosterform will be {b, e, t, r}