NCERT Exercise 1.1 Q10 - Relations and Functions
Question: Give an example of a relation which is (i) symmetric but neither reflexive nor transitive; (ii) transitive but neither reflexive nor symmetric; (iii) reflexive and symmetric but not transitive; (iv) reflexive and transitive but not symmetric; (v) symmetric and transitive but not reflexive.
Answer: (i) {(1,2),(2,1)} on {1,2,3}. (ii) {(1,2),(2,3),(1,3)} on {1,2,3}. (iii) {(1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2)} on {1,2,3}. (iv) ≤ on R. (v) {(1,1),(1,2),(2,1),(2,2)} on {1,2,3} (3 not related...
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