A) (a, b ) R (c,d) if ad (b + c) = be ( a + d)
B) (a, b) R (c, d) if a + d = b + c
C) (a,b) R (c,d) if ad = bc
D) All the above
Correct Answer: D
Solution :
The relation in [A] is reflexive because ab = ba and a + b = b + a, so that ab (b + a) = ba (a + b ). i.e. (a, b) R(a, b). It is also symmetric because ad(b + c) = bc(a + d), i.e. (a,b) R(a, d). Implies cd (d + a) = da(c + b),i.e,., (c, d) R ,(a, b). Simple computations show that relation is TRANSITIVE, too, and that the relations in and are also reflexive, symmetric and transitive.You need to login to perform this action.
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