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Let the no. of elements in a set be denoted by |S|. 

Let |S| contains n elements , then |SxS| = n2

SxS = { (1,1),(1,2),(1,3)........................(1,n)

             (2,1),(2,2)................................(2,n)

            .......................................................

            (n,1),(n,2),..............................(n,n)}

In the cross product of the set, there are n diagonal elements i.e. (1,1),(2,2)......upto (n,n). These elements can either be present in a symmetric relation or absent . Hence for n such elements, there are 2n combinations. 

Among the remaining elements , i.e. n2-n, pair of elements will form a symmetric set for eg (1,2),(2,1) ; (1,3),(3,1) and so on . Hence (n2-n)/2 pairs will contribute to the formation of symmetric sets . 

Hence total number of symmetric sets possible on a set with n elements would be 2n  * 2(n^2-n)/2

Hence for 4 elements as given in the question, there would be 24  * 2(4^2-4)/2

= 24 * 26 = 210 symmetric sets of B 

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