Insert ⊆ or s in each blank to make the resulting statement true....

Question

Insert ⊆ or s in each blank to make the resulting statement true. ∅ ____ ∅

Accepted Answer

Welcome back. I am so glad you're here. We are asked to determine whether an empty set is or is not a subset of an empty set. So an empty set. We recall from previous lessons that an empty set is a set that contains nothing. And these two symbols here in the instructions, whether it is a subset or not, a subset is what will be filling in in between on that black line. So how do we know if something is a subset or not? Well, the first thing is a subset of the second thing if every element, every part of the first set is contained within the second set. So is everything from our first empty set also contained within our second empty set? Yes, it is. So this is a subset. An empty set is a subset of an empty set. Now, if this is still a little bit confusing because they're empty sets, they don't contain anything. There are two things that we need to remember about subsets. First, every set is a subset of itself. So an empty set is a subset of itself. Now, another thing, in case this is still a little bit confusing. It's good to know that every empty set is a subset of every set. So it really didn't even matter what's on the right hand side. Every empty set is a subset of any set that you could put on the right hand side. So we look at our answer choices and this matches with answer choice. A well done. We'll catch you on the next one

Insert ⊆ or s in each blank to make the resulting statement true. ∅ ____ ∅

Key Concepts

Subset

Empty Set

Set Notation

Watch next