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# Is the following set {x: x is a factor of 27} $\ne$ {3, 9, 27, 54}? Give reason.  Hint: Set builder form of a set x is given. We have to understand the given condition on the set x to solve this problem.

The set will have the elements as the factors of 27. But 54 is not a factor of 27.
So, The sets are not equal.
$\therefore$ {x: x is a factor of 27} $\ne$ {3, 9, 27, 54}

Note: A set is a collection of things. We can build a set by describing what is in it. This way of describing a set is set-builder form. Whereas, Roster form is a way to show the elements of a set by listing the elements inside brackets. In the given problem, the set-builder form of x is given on condition that set x should only contain the elements that must be a factor of 27. Factors of 27 are 3, 9 and 27 only. But if we observe the RHS side, the set contains the element 3, 9, 27 and 54. Here the set contains one element which is not satisfying the given condition i.e., 54 is not a factor of 27. So those two sets are not equal.
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