Let R be the relation ''greater than'' from `A={1,4,5}` to `B={1,2,4,5,6,7}`. Write down the elements corresponding to R.

Answer

To solve the problem, we need to find the pairs (a, b) such that a is from set A and b is from set B, and a is greater than b.

### Step-by-Step Solution:

1. **Identify the Sets**:
- Set A = {1, 4, 5}
- Set B = {1, 2, 4, 5, 6, 7}

2. **Formulate the Relation**:
- We are looking for pairs (a, b) where a ∈ A and b ∈ B, and the condition a > b holds.

3. **Check Each Element of A Against Elements of B**:
- For a = 1:
- 1 > 1? No
- 1 > 2? No
- 1 > 4? No
- 1 > 5? No
- 1 > 6? No
- 1 > 7? No
- No pairs for a = 1.

- For a = 4:
- 4 > 1? Yes → (4, 1)
- 4 > 2? Yes → (4, 2)
- 4 > 4? No
- 4 > 5? No
- 4 > 6? No
- 4 > 7? No
- Pairs for a = 4: (4, 1), (4, 2)

- For a = 5:
- 5 > 1? Yes → (5, 1)
- 5 > 2? Yes → (5, 2)
- 5 > 4? Yes → (5, 4)
- 5 > 5? No
- 5 > 6? No
- 5 > 7? No
- Pairs for a = 5: (5, 1), (5, 2), (5, 4)

4. **Compile the Relation R**:
- From the checks above, we have the following pairs:
- From a = 4: (4, 1), (4, 2)
- From a = 5: (5, 1), (5, 2), (5, 4)

5. **Final Result**:
- The elements corresponding to the relation R (greater than) are:
- R = {(4, 1), (4, 2), (5, 1), (5, 2), (5, 4)}