GO Classes Test Series 2024 | Discrete Mathematics | Test 2 | Question: 7

Answer 1

lets assume  A = {1,2,3,4}

Given that, A relation is said to be triangular iff aRb and cRb ==> aRc for all a,b,c belongs to A

Option A, B) S = {(1,1),(2,2),(3,3),(4,4),(1,2),(2,1)} ===> equivalence relation.

               Now we have to check whether it is reflexive and triangular relation

               {(1,1),(2,2),(3,3),(4,4)} ====> reflexive relation.

               (1,1), (2,1) ==> (1,2) is present in S

               (2,2), (1,2) ==> (2,1) is present in S

               so it is triangular relation.

option A ,B) is True.

Option C) S = {(1,2),(2,1),(2,2)} is symmetric and triangular relation.

               how triangular relation is shown below

               (1,2), (2,2) ==>  (1,2) is present in S

                (2,2), (1,2) ==> (2,1) is present in S

           But S is not transitive relation. (1,2),(2,1) ==> (1,1)  is missing

option C) should be False.

Option D) S = {(4,2),(2,1),(4,1),(2,4)} is transitive and triangular relation.

                   but not symmetric relation. (1,2), (1,4) are missing.

Option D) should also be False.

Comments

@GO Classes 

option -C) should be False

A={a,bc}
S={(a,b),(b,a)}  

S is symmetric and triangular but not TRANSITIVE
 

---

Answer Corrected.

---

Deepak Poonia sir i have shown directed edge between nodes (ie elements) if they r related. This relation is reflexive as well as it’s triangular. But it’s not equivalence. Shdn’t this make option A one of the answers?

Edit: no it's not triangular because bRb and cRb is true but bRc is false. Ans A wont be one of the answers