1. Symmetric banane ke liye: Hame (b,a) aur (c,b) add karna hoga.
Ab relation: R1={(a,b),(b,c),(b,a),(c,b)}
2. Transitive banane ke liye: * (a,b) aur (b,c)∈R1⟹ (a,c) add karein.
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(c,b) aur (b,a)∈R1⟹ (c,a) add karein.
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(a,b) aur (b,a)∈R1⟹ (a,a) add karein.
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(b,c) aur (b,a) ke combinations se ⟹ (b,b) aur (c,c) add karein.
3. Final Relation (Rfinal): Symmetry aur Transitivity dono maintain karne ke liye humein ise ek Equivalence Relation banana hoga:
Rfinal={(a,a),(b,b),(c,c),(a,b),(b,a),(b,c),(c,b),(a,c),(c,a)}
4. Calculation: * Total elements in Rfinal=9
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Original elements in R=2
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Added elements =9−2=7
Correct Option: (4) 7