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For the relations R1,R2,R3,R4R_1, R_2, R_3, R_4 defined on the set A={1,2,3}A = \{1,2,3\},

Match the LIST-I with LIST-II

LIST-ILIST-II
A. R1={(1,2),(2,1),(3,3)}R_1 = \{(1,2),(2,1),(3,3)\}I. Transitive only
B. R2={(1,1),(2,2),(3,3)}R_2 = \{(1,1),(2,2),(3,3)\}II. Neither reflexive nor symmetric nor transitive
C. R3={(1,2),(2,3),(1,3)}R_3 = \{(1,2),(2,3),(1,3)\}III. Symmetric but neither reflexive nor transitive
D. R4={(3,3),(3,1),(1,2)}R_4 = \{(3,3),(3,1),(1,2)\}IV. Equivalence

Choose the correct answer from the options given below:

Solution

✅ Correct Option: 4

R1R_1 is symmetric but (1,1)(1,1) is missing and (1,2),(2,1)(1,2),(2,1) do not force (1,1)(1,1), so III.

R2R_2 is the identity relation, hence an equivalence relation, IV.

R3R_3 is transitive only, I.

R4R_4 fails reflexivity, symmetry and transitivity (no (3,2)(3,2)), so II.

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