Q. 14.3( 6 Votes )

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

Answer :

The equivalence class [(1,3)] is the set {(c,d) : (1,3)R(c,d)}


Now as it is given that (a,b)R(c,d) iff a + d = b + c


Hence (1,3) R(c,d) iff 1 + d = 3 + c


(1,3) R(c,d) iff d – c = 2


Now as the set A contains {1, 2, 3, 4} hence we have only two pairs of (c, d) such that d – c = 2 which are (1, 3) and (2, 4)


Hence (1, 3) R (1, 3) and (1, 3)R(2, 4)


Hence the equivalence class [(1,3)] is the set {(1,3), (2,4)}


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