To solve this problem, we need to match each set with the correct description. We will examine each set and each description to determine the correct pairs.
Step-by-step solution:
1. Identify Set (A):
[tex]\(\{1, 2, 3, 6\}\)[/tex]
- These numbers are all divisors of 6.
2. Identify Set (B):
[tex]\(\{T, R, I, G, O, N, M, E, Y\}\)[/tex]
- These are all letters that appear in the word "TRIGONOMETRY".
3. Identify Set (C):
[tex]\(\{2, 3\}\)[/tex]
- These numbers are prime numbers and also divisors of 6.
4. Identify Set (D):
[tex]\(\{1, 3, 5, 7, 9\}\)[/tex]
- These numbers are all odd and less than 10.
Next, we need to map these sets to the correct descriptions:
1. Description (i):
[tex]\(\{y: y \text{ is a divisor of 6 and also a prime number}\}\)[/tex]
- The prime divisors of 6 are [tex]\(\{2, 3\}\)[/tex], which corresponds to Set (C).
2. Description (ii):
[tex]\(\{y: y \text{ is less than 10 and also an odd number}\}\)[/tex]
- The numbers less than 10 and odd are [tex]\(\{1, 3, 5, 7, 9\}\)[/tex], which corresponds to Set (D).
3. Description (iii):
[tex]\(\{y: y \text{ is a natural number divisor of 6}\}\)[/tex]
- The natural number divisors of 6 are [tex]\(\{1, 2, 3, 6\}\)[/tex], which corresponds to Set (A).
4. Description (iv):
[tex]\(\{y: y \text{ is a letter of the word TRIGONOMETRY}\}\)[/tex]
- The letters of the word "TRIGONOMETRY" are [tex]\(\{T, R, I, G, O, N, M, E, Y\}\)[/tex], which corresponds to Set (B).
Therefore, the correct matches are:
- (A) [tex]\(\{1, 2, 3, 6\}\)[/tex] matches with (iii) (natural number divisors of 6).
- (B) [tex]\(\{T, R, I, G, O, N, M, E, Y\}\)[/tex] matches with (iv) (letters of the word TRIGONOMETRY).
- (C) [tex]\(\{2, 3\}\)[/tex] matches with (i) (divisors of 6 that are also prime numbers).
- (D) [tex]\(\{1, 3, 5, 7, 9\}\)[/tex] matches with (ii) (numbers less than 10 and odd).
Thus, the answer is:
- [tex]\(A \rightarrow (iii)\)[/tex]
- [tex]\(B \rightarrow (iv)\)[/tex]
- [tex]\(C \rightarrow (i)\)[/tex]
- [tex]\(D \rightarrow (ii)\)[/tex]
Representing this numerically, we obtain:
- [tex]\(A \rightarrow 3\)[/tex]
- [tex]\(B \rightarrow 4\)[/tex]
- [tex]\(C \rightarrow 1\)[/tex]
- [tex]\(D \rightarrow 2\)[/tex]
Hence, the numerical answer is [tex]\([3, 4, 1, 2]\)[/tex].
