Question Video: Finding Unknown Elements Using the Equality of Sets | Nagwa Question Video: Finding Unknown Elements Using the Equality of Sets | Nagwa

# Question Video: Finding Unknown Elements Using the Equality of Sets Mathematics

If {4๐} โ  {44}, what are the possible values of ๐?

02:25

### Video Transcript

If a set containing the element four ๐ is not equal to a set containing the element 44, what are the possible values of ๐?

The first set thatโs mentioned in our problem is a set containing the element four ๐. Now, when we see a letter written like this, we know that this means four lots of something we donโt know, four lots of ๐. Letโs use this bar model to represent the first set. But what is our set worth? This is quite an interesting problem because often weโll be given an expression like four ๐. And then weโll be told what itโs equal to. And weโll have to use that to work out what ๐ is worth.

But in this problem, weโre not told what four ๐ is equal to. Weโre told what itโs not equal to. And what itโs not equal to is a set containing the element 44. So perhaps the only thing we can do with our bar model is to complete it in a way thatโs not correct. Four ๐ does not have a value of 44. If the set was worth 44, then we could find the value of ๐ by dividing 44 by four. There are four lots of ๐ in 44. We know that 10 fours are in 40. And so there must be 11 fours in 44. And so, in this example, which we know of course is not correct, then ๐ would be equal to 11. Of course, we know this is not true.

So the only thing we do know about ๐ is that is not going to be equal to 11. This is an unusual question because we canโt give one number as an answer. The only answer that we can give is that ๐ can be any number except 11. If the value of ๐ was 11, then we know that the total value of the set would be 44. And weโre told in the question that four ๐ is not equal to 44. So, in a way, instead of saying what ๐ is worth, weโve answered the question by saying what itโs not worth. ๐ can be any number except 11.

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