The image contains set theory and relation-related mathematical problems. Here is a breakdown of the key points:

1. Sets Definitions:

   • $A = \{ x \in \mathbb{Z} : 2 \leq x < 7 \}$: This represents a set of integers $x$ such that $x$ is between 2 and 7, including 2 but not 7.
   • $B = \{2, 7\}$: This set simply contains the integers 2 and 7.
   • $R = \{ (x, y) : x - 1 < y \}$: This defines a relation $R$ such that for any ordered pair $(x, y)$, $x - 1$ must be less than $y$.

2. Interpretation of the Relations:

   • The image also contains examples or specific evaluations of the sets and the relation $R$. For instance:
     • $(2 + 1, 7 - 1) = (2 + 1, 7 - 1)$, which evaluates specific values within a relation or checks a condition.

3. Questions (a), (b), (c):

   • These questions likely ask about verifying certain properties of sets $A$, $B$, and relation $R$.
     • (a) Might involve finding elements in $A$ that satisfy the relation in $R$ when paired with elements from $B$.
     • (b) Might examine properties of elements in $B$ with respect to relation $R$.
     • (c) Likely asks about proving or finding specific pairs in $R$ based on the criteria provided.

Would you like detailed solutions to any specific part of this question? Here are five related questions for further exploration:

1. How would you list all elements in set $A$ as defined?
2. What ordered pairs in $R$ satisfy the condition $x - 1 < y$ using elements from $A$ and $B$?
3. Can you describe the intersection or union of sets $A$ and $B$?
4. How would the condition $x - 1 < y$ change if we altered it to $x - 1 \leq y$?
5. How can we represent $R$ as a matrix if we consider it over a finite set of elements?

Tip: When working with relations, always check if they meet the criteria for properties like reflexivity, symmetry, or transitivity if asked.