# Math Help - proving reflexive, antisymmetric and transitive

1. ## proving reflexive, antisymmetric and transitive

Let A = {1, 2, 3, 4, 5, 6} and let R be the relation on the power set of A defined by X R Y iff X is a subset of Y .
(a) Prove that R is reflexive, antisymmetric, and transitive.
(b) How many ordered pairs are in R? (Hint: For a subset X of size m, how many subsets
Y satisfy XRY ?)

2. Are you having any difficulty in proving (a)?

3. ## proving reflexive, antisymmetric and transitive

yes I am having difficulty.

4. Originally Posted by sbankica
Let A = {1, 2, 3, 4, 5, 6} and let R be the relation on the power set of A defined by X R Y iff X is a subset of Y .
(a) Prove that R is reflexive, antisymmetric, and transitive.
Reflexive: Is each set a subset of itself?

Antisymmetric: If $X \subseteq Y\;\& \;Y \subseteq X$ then what can you conclude?

Transitive: If $X \subseteq Y\;\& \;Y \subseteq Z$ then what can you conclude?