Is empty set part of every set?

by sozener1
Tags: None
 P: 11 you have a power set of s represented by p(s) and s is { x is integer and either x=<-2 or x>=5} and you have another set d = {{-3 -2 1}, {4}, {6, 7}, {-5, 6, 9}} when you are asked for intersection of p(s) and d in a plain maths question am I meant to include { } the empty set as well since it is a subset of everyset???
P: 928
 Quote by sozener1 you have a power set of s represented by p(s) and s is { x is integer and either x=<-2 or x>=5} and you have another set d = {{-3 -2 1}, {4}, {6, 7}, {-5, 6, 9}} when you are asked for intersection of p(s) and d in a plain maths question am I meant to include { } the empty set as well since it is a subset of everyset???
The empty set is a subset of every set. But it is not an element of every set.

In the question above, how many elements are in set d? Of those elements, which are members of p(s)?
P: 83
 Quote by sozener1 you have a power set of s represented by p(s) and s is { x is integer and either x=<-2 or x>=5} and you have another set d = {{-3 -2 1}, {4}, {6, 7}, {-5, 6, 9}} when you are asked for intersection of p(s) and d in a plain maths question am I meant to include { } the empty set as well since it is a subset of everyset???
{} is a subset of every set, so it is a subset of s. Therefore, {} is an element of p(s). However, it is clear that {} is not in set d. Therefore, {} is not an element of the intersection of p(s) and d.