Question

Which of the following are finite sets *

The set of all x such that x is a prime number which is a divisor of 60

The set of all points in a plane

The set of all letters in the word TRIGONOMETRY​

Answer 1

a)

D={x:x is a prime number which is a divisor of 60}

The divisors of 60 are 1,2,3,4,5,6,10,12,15,20,30,60.

The prime divisors of 60 are 2,3,5. So, the answer is 2,3 5.

b)

A circle is the set of all points in a plane that are equidistant from a given point called the center of the circle. ... The a line segment from the center of the circle to any point on the circle is a radius of the circle. By definition of a circle, all radii have the same length.

c)

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 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 letters T, R, and O are repeated.

Answer 2

(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}