Symmetric relation

Step 1: To form the reverse pair, interchange the first and second entries. Step 2: Reversing ((8,5)) gives ((5,8)). Step 3: This small step is the key in symmetry questions.

Step 1: ((2,1)) is present for ((1,2)). Step 2: ((4,3)) is present for ((3,4)). Step 3: If every pair has its reverse, the relation is symmetric.

Step 1: ((1,2)) and ((2,1)) are reverse pairs. Step 2: The reverse of ((1,3)), which is ((3,1)), is not given. Step 3: Identifying incomplete pairs is the fastest way to check symmetry.

Step 1: The rule of symmetry directly applies to the reverse pair. Step 2: The required reverse pair for ((p,q)) is ((q,p)). Step 3: Do not assume ((p,p)) or ((q,q)) unless given or required by another condition.

Step 1: A symmetric example must contain a pair along with its reverse. Step 2: Option A has both ((1,2)) and ((2,1)). Step 3: Even in small examples, do not forget to match reverse pairs.

Step 1: In a symmetric relation, the reverse of every ordered pair must also be in the relation. Step 2: ((1,4)) is matched by ((4,1)), and ((2,2)) reverses to itself. Step 3: In such questions, first make pairs of reverse ordered pairs.

Step 1: For symmetry, reverse the given ordered pair. Step 2: The reverse of ((10,3)) is ((3,10)). Step 3: Symmetry guarantees only the reverse pair, not all other related pairs.

Step 1: ((1,2)) and ((2,1)) are already reverse pairs. Step 2: The reverse of ((3,2)), which is ((2,3)), is missing. Step 3: To make a relation symmetric, add only the missing reverse pair.

Step 1: In a symmetric relation, every pair with different entries must have its reverse pair. Step 2: Option B has ((1,3)) with ((3,1)), and ((2,2)) reverses to itself. Step 3: To solve options quickly, look for missing reverse pairs.

Step 1: The reverse of ((1,1)) is itself. Step 2: ((1,2)) is matched by ((2,1)), and ((2,3)) is matched by ((3,2)). Step 3: Symmetry does not require all ((a,a)) pairs to be present.

Step 1: If (a-b) is even, then its negative (b-a) is also even. Step 2: So whenever ((a,b)) satisfies the rule, ((b,a)) also satisfies it. Step 3: For rule-based relations, check whether the reversed pair satisfies the same rule.

Step 1: If (|a-b|=1), then reversing the order gives (|b-a|=1) as well. Step 2: Therefore, if ((a,b)) is in the relation, ((b,a)) is also in it. Step 3: Rules involving absolute difference often produce symmetry.

Step 1: In option D, ((2,3)) is matched by ((3,2)). Step 2: But the reverse of ((1,2)), which is ((2,1)), is missing. Step 3: If even one pair is missing its reverse, the relation is not symmetric.

Step 1: Reversing ((5,5)) gives ((5,5)) again. Step 2: Reversing ((7,7)) gives ((7,7)) again. Step 3: Pairs with the same entries satisfy the symmetry condition.

Step 1: Symmetry is related to the order of entries in a pair. Step 2: So we must check whether ((b,a)) is present for every ((a,b)). Step 3: Do not decide only by counting the number of pairs.

Step 1: ((1,1)) and ((3,3)) are their own reverses. Step 2: ((2,3)) is matched by ((3,2)). Step 3: Since all pairs have their reverses, the relation is symmetric.

Step 1: The reverse of ((2,5)) is ((5,2)). Step 2: A symmetric relation must contain this reverse pair. Step 3: If the reverse pair is missing, the relation cannot be symmetric.

Step 1: The main idea in a symmetric relation is the reverse pair. Step 2: So if ((a,b)) is present, ((b,a)) must be present. Step 3: In exams, do not fear symbolic notation; just reverse the order of the pair.

Step 1: The pair ((1,2)) is already matched by ((2,1)). Step 2: The reverse of ((3,4)), which is ((4,3)), is missing. Step 3: Adding the reverse of the incomplete pair will make the relation symmetric.

Step 1: Same parity means both numbers are even or both are odd. Step 2: If (x) and (y) have the same parity, then (y) and (x) also have the same parity. Step 3: Rules that remain true in both directions give symmetry.