The probability that a relation R from x , y to x , y is both symmetric and transitive, is equal to:

Step-by-step solution

Total number of elements in the Cartesian product will be 4 , so total possible relations will be 2 4 = 16 The relations which will be symmetric and transitive both will be ,   x , x ,   y , y ,   x , x , y , y ,   x , x , x , y , y , x y , y i.e. 5 relations Hence, required probability will be 5 16