It seems like you've uploaded an image containing a set of mathematical problems and relational questions. I’ll walk through one of the questions based on the parts I can see clearly.

22a (ii) appears to ask you to determine whether each of the following relations on the set $\{1, 2, 3, 4\}$ is reflexive, symmetric, antisymmetric, and transitive. The relations listed are:

1. $R_1 = \{(2, 1), (3, 2), (3, 3)\}$
2. $R_2 = \{(1, 1), (2, 2), (3, 3), (4, 4)\}$
3. $R_3 = \{(1, 2), (2, 1), (2, 3), (3, 4)\}$
4. $R_4 = \{(1, 1), (2, 2), (3, 3), (4, 4), (1, 2), (2, 3), (3, 4)\}$
5. $R_5 = \{(1, 3), (2, 2), (3, 3), (4, 4)\}$

Let's analyze one of these relations as an example.

Example: $R_1 = \{(2, 1), (3, 2), (3, 3)\}$

1. Reflexive: For a relation to be reflexive, every element in the set must relate to itself. The set is $\{1, 2, 3, 4\}$, so we need the pairs $(1, 1), (2, 2), (3, 3), (4, 4)$. Since $(2, 2)$ and $(1, 1)$ are missing, it is not reflexive.

2. Symmetric: A relation is symmetric if whenever $(a, b) \in R$, then $(b, a) \in R$. In $R_1$, we have $(2, 1)$ but not $(1, 2)$, so it is not symmetric.

3. Antisymmetric: A relation is antisymmetric if for any $(a, b) \in R$ and $(b, a) \in R$, then $a = b$. There is no pair such that both $(a, b)$ and $(b, a)$ appear in $R_1$, so the relation is antisymmetric.

4. Transitive: A relation is transitive if whenever $(a, b) \in R$ and $(b, c) \in R$, then $(a, c) \in R$. There’s no situation where we can verify a transitive property in $R_1$, so it is transitive.

Would you like me to analyze the remaining relations or assist with another part of the image?

Here are 5 related questions for practice:

1. How do you prove if a relation is an equivalence relation?
2. What is the difference between symmetric and antisymmetric relations?
3. Can a relation be both symmetric and antisymmetric? If yes, under what conditions?
4. How would you check if a relation is a partial order?
5. How does the concept of transitivity apply in real-world relations like "is a parent of"?

Tip: When determining whether a relation is reflexive, always check if every element relates to itself (i.e., $(a, a)$ should be in the set for all elements $a$).