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Discrete Mathematics With Applicat...
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Discrete Mathematics With Applicat...
In 9-33, determine whether the given relation is reflexive, symmetric, transitive, or none of these. Justify your answer.
Let X be a nonempty set and
To justify whether the given relation is reflexive, symmetric, transitive, or none of these.
Given information:
Let X be a nonempty set and P(X) the power set of X. Define the “not equal to” relation U on P(X) as follows: For all A, B ∈ P(X), A U B ⇔
Calculation:
Reflexive:
The relation U is reflective if
Since
We note that U does not contain
Symmetric:
The relation U on a set A is symmetric if
Let us assume that
Chapter 8 Solutions
