Video: Finding Unknown Elements Using the Equality of Sets

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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