Question

8. Which of the following is written in Set Builder Notation? = {x|x is a set of A = Oletter in the word MATH} Set A is a set of letters in the word MATH. The set of letters in the word MATH O A= {M, A, T, H}​

Answer 1

Step-by-step explanation:

Set-builder notation is the mathematical notation for describing a set by stating all the properties that the elements in the set must satisfy. The set is written in this form: {variable ∣ condition1, condition2,...}. The bar in the middle can be read as "such that".

Answer 2

Answer:

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}