Consider the following sets :
`phi,A={1,3},B={1,5,9},C={1,3,5,7,9}`.
Insert the correct symbol `subor!in` between each pair of sets : (i) `phi……B`
(ii) A……..B
(iii) A……… C
(iv) B……..C.

Answer

To solve the problem, we need to determine the correct relationship between the given sets using the symbols for subset (⊆) and not a subset (⊄). Let's analyze each pair of sets step by step.

### Given Sets:
- \( \phi \) (empty set)
- \( A = \{1, 3\} \)
- \( B = \{1, 5, 9\} \)
- \( C = \{1, 3, 5, 7, 9\} \)

### Step-by-Step Solution:

1. **(i) \( \phi \) and \( B \)**:
- The empty set \( \phi \) is a subset of every set, including \( B \).
- Therefore, the relationship is:
\[ \phi \subseteq B \]

2. **(ii) \( A \) and \( B \)**:
- The elements of \( A \) are \( 1 \) and \( 3 \).
- The elements of \( B \) are \( 1, 5, 9 \).
- The element \( 3 \) is not present in \( B \).
- Therefore, the relationship is:
\[ A \not\subseteq B \]

3. **(iii) \( A \) and \( C \)**:
- The elements of \( A \) are \( 1 \) and \( 3 \).
- The elements of \( C \) are \( 1, 3, 5, 7, 9 \).
- Both elements \( 1 \) and \( 3 \) are present in \( C \).
- Therefore, the relationship is:
\[ A \subseteq C \]

4. **(iv) \( B \) and \( C \)**:
- The elements of \( B \) are \( 1, 5, 9 \).
- The elements of \( C \) are \( 1, 3, 5, 7, 9 \).
- All elements of \( B \) are present in \( C \).
- Therefore, the relationship is:
\[ B \subseteq C \]

### Final Answers:
1. \( \phi \subseteq B \)
2. \( A \not\subseteq B \)
3. \( A \subseteq C \)
4. \( B \subseteq C \)