0 votes 0 votes given a relation on R on the set A={1,2,3,4} in the form of matrix representation as , $M_R$=$\begin{bmatrix} 0 & 1 & 0 & 0\\ 0& 0& 1 &0 \\ 0& 0& 0 &1 \\ 0& 0& 0& 0 \end{bmatrix}$ Then the cardinality of the smallest equivalence relation on A which contains R is equal to answer given-16 Prateek Raghuvanshi asked Jan 12, 2019 edited Jan 12, 2019 by Prateek Raghuvanshi Prateek Raghuvanshi 445 views answer comment Share Follow See all 6 Comments See all 6 6 Comments reply Magma commented Jan 12, 2019 reply Follow Share 16 is the correct answer 0 votes 0 votes Prateek Raghuvanshi commented Jan 12, 2019 reply Follow Share can you please express your approach. 0 votes 0 votes Magma commented Jan 12, 2019 reply Follow Share (1,1) , (2,2) , (3,3) , (4,4) , (1,2) , (2,3) , (3,4) --- > matrix representation (2,1) , (3,2) , (4,3) --> build that relation into symmetric relation (2,4) , ( 1,3) , (4,2) , (3,1) , (1,4), (4,1) ---- > transitive relation 1 votes 1 votes Magma commented Jan 12, 2019 reply Follow Share @Prateek Raghuvanshi you didn't the condition where (2,3) ,(3,4) , [ (2,4) --- > As per transitive rule ] 1 votes 1 votes Kunal Kadian commented Jan 12, 2019 reply Follow Share You will also have to add (1,3),(2,4)(3,1)(4,2),(1,4),(4,1).. and also all reflexive relations 0 votes 0 votes Prateek Raghuvanshi commented Jan 12, 2019 reply Follow Share @ Magma thank you ,i got what i did mistake . 1 votes 1 votes Please log in or register to add a comment.
2 votes 2 votes Given adjacency from the matrix: (1,2) (2,3) (3,4) to satisfy reflexive: adding (1,1) (2,2) (3,3) (4,4) to satisfy symmetric: adding (2,1) (3,2) (4,3) to satisfy transitive: adding (1,3) (2,4) (4,2) (3,1) (1,4) (4,1) Hence, the cardinality is 16 balchandar reddy san answered Jan 12, 2019 balchandar reddy san comment Share Follow See all 0 reply Please log in or register to add a comment.