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Let s={1, 2, 3, 4} and A=S X S. define the following relation:- R on A : (a, b)R (a', b') if only if a+b=a'+b'. (i) Show that r is an equivalence relation. (ii) Compute A/R
written 7.4 years ago by gravatar for teamques10 teamques10 ★ 65k modified 2.3 years ago by gravatar for pedsangini276 pedsangini276 • 4.8k

Mumbai University > Computer Engineering > Sem 3 > Discrete Structures

Marks: 6 Marks

Year: Dec 2013
discrete mathematics
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written 7.4 years ago by gravatar for teamques10 teamques10 ★ 65k •   modified 7.4 years ago

  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, …

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