Write the following sets in the form of lists: (i) {x:x is a prime number and 1<x>100}
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Answer:(i) A={x:x is an integer and−3<x<7}
The elements of this set are −2,−1,0,1,2,3,4,5, and 6 only.
Therefore, the given set can be written in roster form as
A={−2,−1,0,1,2,3,4,5,6}
(ii) B={x:x is a natural number less than 6}
The natural numbers less than 6 are 1,2,3,4,5
So, the elements of this set are 1,2,3,4, and 5 only.
Therefore, the given set can be written in roster from as
B={1,2,3,4,5}
(iii) C={x:x is a two-digit natural number such that the sum of its digits is 8}
The elements of this set are 17,26,35,44,53,62,71 and 80 only.
Therefore, this set can be written in roster form as
C={17,26,35,44,53,62,71,80}
(iv) D={x:x is a prime number which is a divisor of 60}
2∣60
2∣30
3∣15
5∣5
∣1
∴60=2×2×3×5
∴ The elements of this set are 2,3, and 5 only.
Therefore, this set can be written in roster form as D={2,3,5}.
(v) E= The set of all letters in the word TRIGONOMETRY
There are 12 letters in the word TRIGONOMETRY, out of which the letters, T, R, and O are repeated. And we write the repeated letters once only.
Therefore, this set can be written in roster form as
E={T,R,I,G,O,N,M,E,Y}
(vi) F= The set of all letters in the word BETTER
There are 6 letters in the word BETTER, out of which letters E and T are repeated.
Therefore, this set can be written in roster form as
F={B,E,T,R}
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