Video: Finding the Relation between Two Given Sets

Use ⊂ or ⊄ to fill in the gap {3} _ {3, 4}.

02:13

Video Transcript

Use the symbol for “is a subset of” or the symbol for “is not a subset of” to fill in the gap. The set containing the element three, what, a set containing the elements three and four.

Before we answer the question, let’s remind ourselves what these two symbols mean. Because if we don’t understand what they represent, then we’re going to find it difficult to read the question let alone answer it. These are the symbols we use when something is or is not a subset of something else.

If we imagine this circle representing a set and everything inside the circle is part of that set, then this smaller circle inside it is a subset of the larger set. And so the two symbols in the question are all about whether something is a subset or not a subset of a set. The first symbol means “is a subset of”, and we use the second symbol if something is not a subset of something else. So let’s use these facts to help us to solve the problem.

In the question, we’re given two sets. The first contains the number three, and the second set contains the numbers three and four. And what the question is asking us is, is the set containing the number three a subset of the set containing the numbers three and four? Let’s imagine our circles again. We know the largest set contains the numbers three and four. But can we now make a subset of this, just containing the number three? Yes, we can.

The number three is a subset of the numbers three and four. And if we look at the notation for the two sets, we can see the number three there. It’s part of the larger set, and so we can complete the statement using this symbol. A set containing the element three is a subset of a set containing the elements three and four.

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