Answer
Not Reflexive
Not Symmetric
Transitive
Work Step by Step
Let X = {a, b, c} and P(X) be the power set of X.
A relation L is defined on P(X) as follows: For all
A, B ∈ P(X), A L B ⇔ the number of elements in A is
less than the number of elements in B.
Reflexive: for all B $\in$ P(X) BLB,
the statement is false since it invalidates the relation L since a set has the same number of elements of the set itself.
Symmetric: for all A, B $\in$ P(X) if ALB then BLA
assume that ALB is true which means set A has fewer elements than set B
which means that BLA is false since set b has more elements than A.
Transitive: for all A, B, and C $\in$ P(X) if ALB AND BLC then ALC.
ALB <=> A B
