Question

Symmetric relation are closed under complementation

Answer 1

It is a contradiction

Step-by-step explanation:

Symmetric relation are closed under complementation

A relation R' is the symmetric closure of a relation R if and only if

(1) R' is symmetric,

(2) R  R', and

(3) for any relation R'', if R  R'', and R'' is symmetric, then R'  R'' , that is, R' is the smallest relation that satisfies (1) and (2).

Example: Let R be the less-than relation on the set of integers I. Then the symmetric closure of R, denoted by s(R) is s(R) = { <a, b> | a  I  b  I  [ a < b  a > b ] } that is { <a, b> | a  I  b  I  a  b }

The digraph of the symmetric closure of a relation is obtained from the digraph of the relation by adding for each arc the arc in the reverse direction if one is already not there.

#Learn more:

Although they are radially symmetric, echinoderms are more closely related to humans than a jellyfish is because they are ______.

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