`x in{2,4,6,9}` and `yin{4,6,18,27,54}`. Form all ordered pairs (x,y) such that x is factor of y and `xley`.

Answer

To solve the problem, we need to find all ordered pairs (x, y) such that x is a factor of y and x ≤ y, where x is taken from the set {2, 4, 6, 9} and y is taken from the set {4, 6, 18, 27, 54}.

### Step-by-Step Solution:

1. **Identify the Sets**:
- Let \( X = \{2, 4, 6, 9\} \)
- Let \( Y = \{4, 6, 18, 27, 54\} \)

2. **Check Each Element of X Against Y**:
- We will check each element \( x \) in \( X \) to see if it is a factor of any \( y \) in \( Y \) and if \( x \leq y \).

3. **For \( x = 2 \)**:
- Check \( y = 4 \): \( 2 \) is a factor of \( 4 \) and \( 2 \leq 4 \) → (2, 4)
- Check \( y = 6 \): \( 2 \) is a factor of \( 6 \) and \( 2 \leq 6 \) → (2, 6)
- Check \( y = 18 \): \( 2 \) is a factor of \( 18 \) and \( 2 \leq 18 \) → (2, 18)
- Check \( y = 27 \): \( 2 \) is not a factor of \( 27 \)
- Check \( y = 54 \): \( 2 \) is a factor of \( 54 \) and \( 2 \leq 54 \) → (2, 54)

4. **For \( x = 4 \)**:
- Check \( y = 4 \): \( 4 \) is a factor of \( 4 \) and \( 4 \leq 4 \) → (4, 4)
- Check \( y = 6 \): \( 4 \) is not a factor of \( 6 \)
- Check \( y = 18 \): \( 4 \) is not a factor of \( 18 \)
- Check \( y = 27 \): \( 4 \) is not a factor of \( 27 \)
- Check \( y = 54 \): \( 4 \) is not a factor of \( 54 \)

5. **For \( x = 6 \)**:
- Check \( y = 4 \): \( 6 \) is not a factor of \( 4 \)
- Check \( y = 6 \): \( 6 \) is a factor of \( 6 \) and \( 6 \leq 6 \) → (6, 6)
- Check \( y = 18 \): \( 6 \) is a factor of \( 18 \) and \( 6 \leq 18 \) → (6, 18)
- Check \( y = 27 \): \( 6 \) is not a factor of \( 27 \)
- Check \( y = 54 \): \( 6 \) is a factor of \( 54 \) and \( 6 \leq 54 \) → (6, 54)

6. **For \( x = 9 \)**:
- Check \( y = 4 \): \( 9 \) is not a factor of \( 4 \)
- Check \( y = 6 \): \( 9 \) is not a factor of \( 6 \)
- Check \( y = 18 \): \( 9 \) is a factor of \( 18 \) and \( 9 \leq 18 \) → (9, 18)
- Check \( y = 27 \): \( 9 \) is a factor of \( 27 \) and \( 9 \leq 27 \) → (9, 27)
- Check \( y = 54 \): \( 9 \) is a factor of \( 54 \) and \( 9 \leq 54 \) → (9, 54)

7. **Compile All Valid Ordered Pairs**:
- From the checks above, the valid ordered pairs are:
- (2, 4)
- (2, 6)
- (2, 18)
- (2, 54)
- (4, 4)
- (6, 6)
- (6, 18)
- (6, 54)
- (9, 18)
- (9, 27)
- (9, 54)

### Final Answer:
The ordered pairs (x, y) such that x is a factor of y and x ≤ y are:
- (2, 4)
- (2, 6)
- (2, 18)
- (2, 54)
- (4, 4)
- (6, 6)
- (6, 18)
- (6, 54)
- (9, 18)
- (9, 27)
- (9, 54)