Sets, Relations & Functions
Minimum elements for symmetric and transitive closure
nta_pyq_2023_jan
Grade 11
The minimum number of elements that must be added to the relation R = \{(a,b),(b,c)\} on the set \{a, b, c\} so that it becomes symmetric and transitive is:
Step-by-Step Solution
Key Concept: For symmetric: add (b,a),(c,b). For transitive: (a,b),(b,c)$\in$R $\Rightarrow$ (a,c) must be in R. Then check all new pairs for further requirements.
Elements to add: (b,a),(c,b),(a,c),(c,a),(a,a),(b,b),(c,c) = 7 elements. Answer: (2) 7
Correct Answer: 2