Mumbai University > Computer Engineering > Sem 3 > Discrete Structures

Marks: 6 Marks

Year: Dec 2013

1. R is an equivalence, if

   a). Reflexive:

   (a, b) R (a’, b’) i.e. a+b=a’+b’ which is true. Hence R is reflexive.

   b) Symmetric:

   (a, b) R (a’, b’) $ \rightarrow a+b’=b+a’ \\ \rightarrow b+a’=a+b’ \rightarrow a’+b=b’+a \rightarrow (a’, b’) R (a, b)$

   Hence relation is symmetric.

   c) Transitive:

   Let (a, b) R (a’, b’) and (a’, b’) R (a’’, b’’) then a+b’=b+a’ and a’+b’’=b’+a’’ then add a+b’+a’+b’’=b+a’+b’+a’’ or a+b’’=b+a’’ or (a, b)R(a’’, b’’) then R is equivalent relation.

2. For A/R

   [1]={1, 2}=[2] [3]={3, 4}=[4].

   Hence, A/R={[1], [3]}.