Set A = {1, 2, 3, 4}, write a binary relation R on A that is...

Set A = {1, 2, 3, 4}, write a binary relation R on A that is reflexive, symmetric and transitive, with (1, 2),(3, 2) ∈ R.

Expert Solution

Here A = { 1,2,3,4 }.

Now we define a binary relation R on A , then R must a subset of A × A.

R = { (1 ,1 ), (2, 2), (3, 3) , (4, 4), (1, 2), (2, 1), (2, 3), (3,2) }.

As R is subset of A × A , therefore it is a binary relation on A with , (1, 2), (3, 2) R.

Clearly ,R is reflexive as for all x A, (x, x)R.

R is also symmetric relation as if (x, y) R (y, x) R for x ,y are member of A.

For any (x, y) R and (y, z) R (x, z) R , for x, y, z are member of A.

Another relation on A can be defined as -

R = { ( 1,1), (2, 2), (3, 3), (4, 4), ( 1, 2) , (2, 1), (2, 3), ( 3, 2), ( 2, 4), (4, 2)}.

This relation R is also reflexive, symmetric and transitive , with ( 1, 2), (3, 2) R.

Colby Messinger answered 6 months ago

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