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# Let R = {(x, y) : x, y A, x + y = 5} where A = {1, 2, 3, 4, 5} then

- R is not reflexive, symmetric and not transitive
- R is an equivalence relation
- R is reflexive, symmetric but not transitive
- R is not reflexive, not symmetric but transitive

## The correct answer is: R is not reflexive, symmetric and not transitive

### To define the given statement.

For the given R= {(x, y) : x, y A, x + y = 5}, R can take the values {(1,4),(4,1),(2,3)(3,2)}

From the values, R is not reflexive since $(1,1)∈/R.$

R is symmetric

R is not transitive as $(1,4)∈R$, $(4,1)∈R$ but $(1,1)∈/R.$

R is symmetric

Hence, the given relation is not reflexive, symmetric and not transitive

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