Solution

The correct answer is (C) and (E) Only

Concept:

To determine which relations are reflexive, we need to check if every element in the set {1, 2, 3, 4} is related to itself. In other words, for a relation to be reflexive, it must contain all pairs (x, x) for each element x in the set.

Given Relations:

1. R1 = {(1, 1), (1, 2), (2, 1), (2, 2), (3, 4), (4, 1), (4, 4)}
    Missing: (3, 3)  Not reflexive.

2. R2 = {(1, 1), (1, 2), (2, 1)}
    Missing: (2, 2), (3, 3), (4, 4) Not reflexive.

3. R3 = {(1, 1), (1, 2), (1, 4), (2, 1), (2, 2), (3, 3), (4, 1), (4, 4)}
    Contains: (1, 1), (2, 2), (3, 3), (4, 4) Reflexive.

4. R4 = {(2, 1), (3, 1), (3, 2), (4, 1), (4, 2), (4, 3)}
    Missing: (1, 1), (2, 2), (3, 3), (4, 4) Not reflexive.

5. R5 = {(1, 1), (1, 2), (1, 3), (1, 4), (2, 2), (2, 3), (2, 4), (3, 3), (3, 4), (4, 4)}
    Contains: (1, 1), (2, 2), (3, 3), (4, 4) Reflexive.

Summary:

• Reflexive Relations: R3, R5
• Not Reflexive Relations: R1, R2, R4

Conclusion:

• The correct answer is: 4) (C) and (E) Only