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Consider  the  set  S  =  {a,  b}  and  ‘L’  be  a  binary  relation  such  that  L  =  {all  binary
relations  except  reflexive  relation  set  S}.  The  number  of  relation  which  are
symmetric _______.
asked in Set Theory & Algebra by (199 points)   | 44 views

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L  =  {all  binary relations  except  reflexive  relation  set  S}

=> L has no xRx pair

=> So no diagonal element present.

=> Total size of L = 2^(n2 - n)

In symmetric relations, xRy and yRx should both come. For each x and y (x!=y), either (x,y) or (y,x) can be present.

Number of symmetric relations in L = (No diagonal element selected)*(One of the non-diagonal pairs)

No of non-diagonal pairs =  (n2 - n)/2 

=> Number of symmetric relations =  2^((n2 - n)/2)

answered by Active (1.6k points)  

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