Sets, Relations & Functions
Equivalence Relations — minimum elements to add
nta_pyq_2023_jan
Grade 11
The minimum number of elements that must be added to the relation R = \{(a, b), (b, c), (b, d)\} on the set \{a, b, c, d\} so that it is an equivalence relation, is _______.
Step-by-Step Solution
Key Concept: An equivalence relation must be reflexive, symmetric, and transitive. Add all missing pairs to satisfy all three properties.
For equivalence relation, R must contain: {(a,a),(b,b),(c,c),(d,d),(a,b),(b,a),(b,c),(c,b),(b,d),(d,b),(a,c),(a,d),(c,d),(d,c),(c,a),(d,a)} — 3 already given, so 13 more to be added. Answer: 13
Correct Answer: 13