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| Math Central | Quandaries & Queries |
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Question from raji, a student: suppose R be a non empty relation on a collection of sets defined by ARB if and only if A intersection B is null set.then.....the correct answer is R is symmetric and not transitive...my doubt is how it is symmetric |
Hi Raji,
A relation $\mathbf{ R}$ on a set $\mathbf{ X}$ is symmetric if it is true that for each $A, B \in \mathbf{ X}$ if $A\mathbf{ R}B$ then $B\mathbf{ R}A.$
Your relation is defined by $A\mathbf{ R}B$ if and only if $A \cap B = \emptyset.$
Suppose $A$ and $B$ are sets in the domain of your relation and $A\mathbf{ R}B$ then $A \cap B = \emptyset.$ What can you say about $B \cap A?$
Penny
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