Answer
-E is reflexive
-E is symmetric
-E is Transitive
Work Step by Step
-AS X ={ a,b,c} and P(X) be the power set of X (the set of all subsets of X).
$(A relation E is defined on P(X) as follows:
For all A, B ∈P(X), A E B ⇔the number of elements in A equals the number of elements in B. )
--E is reflexive:
-E is reflexive⇔for all sub sets A of X, A E A. By definition of E, this means that for all subsets A of X, A has the same number of elements as A. But this is true.
--E is symmetric:
- E is symmetric⇔for all subsets A and B of X, if A E B then B E A. By definition of E, this means that if A has the same number of elements as B, then B has the same number of elements as A. But this is true.
-- E is transitive: E is transitive ⇔ for all subsets A, B, and C of X, if A E B and B E C, then A E C. By definition of E, this means that for all subsets, A, B, and C of X, if A has the same number of elements as B and B has the number of elements as C, then A has the same number of elements as C. But this is true.
