Reflexive relation

Step 1: Each element needs one self-pair. Step 2: For (n) elements, there are (n) such pairs. Step 3: (n^2) is the number of all possible pairs, not the minimum reflexive relation.

Step 1: In (A \times A), each element can appear in the first and second position. Step 2: So total pairs are (n \times n=n^2). Step 3: Reflexive relation needs (n) compulsory pairs, while (A \times A) has (n^2) possible pairs.

Step 1: Reflexivity requires only self-pairs. Step 2: ((1,2)) has two different elements, so it is not compulsory. Step 3: Separate compulsory pairs from optional pairs.

Step 1: Look for the self-pairs of (2,3,4). Step 2: ((2,2),(3,3),(4,4)) are all present, so (R) is reflexive. Step 3: Extra reverse pairs do not affect the reflexive check.

Step 1: The required self-pairs are ((2,2),(3,3),(4,4)). Step 2: ((3,3)) is not present in the given (R). Step 3: In a reflexive relation, every element must be connected to itself.

Step 1: The rule of reflexivity applies to every element. Step 2: If (a \in A), then ((a,a)) must belong to (R). Step 3: In symbol-based questions, focus on self-pairs.

Step 1: (A \times A) contains all ordered pairs from (A). Step 2: Since (2 \in A), ((2,2)) belongs to (A \times A). Step 3: The universal relation is a simple example of a reflexive relation.

Step 1: When (a=b), the ordered pair becomes a self-pair. Step 2: For every (a \in A), ((a,a)) satisfies this rule. Step 3: The relation (a=b) is the identity relation and is reflexive.

Step 1: For reflexivity, check the case (a=a). Step 2: Every number is equal to itself, so (a \le a) is true. Step 3: In inequality relations, first test the equality case.

Step 1: Reflexivity requires ((a,a)). Step 2: The rule (a<b) would require (a<a), which is false. Step 3: Strict inequality relations are usually not reflexive.

Step 1: For reflexivity, put (a=b). Step 2: Then (a-a=0), and 0 is even. Step 3: In difference-based rules, first subtract the element from itself.

Step 1: For a self-pair, take (a=b). Step 2: Then (a-a=0), and 0 is not odd. Step 3: Reflexivity needs self-pairs for all elements.

Step 1: For reflexivity, check whether (a) divides itself. Step 2: Since (a=a \times 1), (a) divides itself. Step 3: In divisibility, remember the self-divisibility case.

Step 1: Reflexivity requires ((a,a)). Step 2: But under (a\ne b), (a\ne a) is false, so self-pairs are absent. Step 3: A not-equal relation is not reflexive.

Step 1: For reflexivity, put ((a,a)) into the rule. Step 2: (a+a=2a) is always even, so every self-pair is included. Step 3: In sum-based rules, quickly test (a+a).

Step 1: For a self-pair, put (b=a) in (a+b). Step 2: (a+a=2a) is even, not odd. Step 3: So this relation is not reflexive.

Step 1: For self-pairs, put (a=b). Step 2: Then (a-a=0), so every ((a,a)) satisfies the rule. Step 3: (a-b=0) represents equality.

Step 1: For reflexivity, compare each number with itself. Step 2: Every number has the same remainder as itself. Step 3: In same-remainder relations, self-pairs always satisfy the rule.

Step 1: For reflexivity, put (a=b). Step 2: For every (a), (a \equiv a \pmod{2}) is true. Step 3: Congruence relations include all self-pairs.

Step 1: Reflexivity needs ((1,1),(2,2),(3,3),(4,4)). Step 2: The rule requires the first element to be even, but (1) is not even, so ((1,1)) is missing. Step 3: Missing one required pair makes it not reflexive.