Determine whether the following relation is reflexive, transitive and symmetric :
R = {(x,y) : x and y work at the same place }

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Solution

) R = {(x, y): x and y work at the same place}

(x, x) ∈ R

∴ R is reflexive.

If (x, y) ∈ R, then x and y work at the same place.

⇒ y and x work at the same place.

⇒ (y, x) ∈ R.

∴ R is symmetric.

Now, let (x, y), (y, z) ∈ R

⇒ x and y work at the same place and y and zwork at the same place.

⇒ x and z work at the same place.

⇒ (x, z) ∈R

∴ R is transitive.

Hence, R is reflexive, symmetric, and transitive.

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Determine whether the following relation is reflexive, transitive and symmetric : R = {(x,y) : x and y work at the same place }

Determine whether the following relation is reflexive, transitive and symmetric :
R = {(x,y) : x and y work at the same place }