Let A = {2, 4, 6, 8, 10, 12}, B = {2, 4, 8, 10}, C = {4, 10, 12},...

Question

Let A = {2, 4, 6, 8, 10, 12}, B = {2, 4, 8, 10}, C = {4, 10, 12}, D = {2, 10}, andU = {2, 4, 6, 8, 10, 12, 14}. Determine whether each statement is true or false. ∅ ⊆ ∅

Accepted Answer

Hello. Today we are asked to determine whether a null set can be a subset of another null set. So just to clarify, this symbol stands for subset. And let's just go ahead and think about what the definition of a subset is. Let's say I have a set of numbers and we're going to call the set of numbers A. A subset is essentially another set of numbers that exists within the current set of numbers. And this subset is going to contain the same elements or the same numbers as the outermost set. A. So you can go ahead and rename this to be a So a can be a subset of a or in other words, a set of numbers can be a subset of itself because both of the sets are going to contain the same amount amount of elements anyway. Now a null set is essentially a set of numbers with an unknown amount of elements, but those elements are empty. So we can represent that set of numbers or the null set as an empty circle. And if I take a smaller set of numbers from within this empty circle, then that's going to be another null set. So a null set can be a subset of another null set because it's going to contain the same amount of elements as a null set. So with that being said, the answer to this problem is going to be a it is true that a no set can be a subset of a no set. So I hope this video helps you in understanding the definition of a subset and I'll go ahead and see you all in the next video.

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Let A = {2, 4, 6, 8, 10, 12}, B = {2, 4, 8, 10}, C = {4, 10, 12}, D = {2, 10}, andU = {2, 4, 6, 8, 10, 12, 14}. Determine whether each statement is true or false. ∅ ⊆ ∅