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Given, $U=\{1,2,3,4,5,6\},A=\{1,2,3\}$. We have to find the complement of the set A.

We start by,

Since set $A=\{1,2,3\}$, so $A'=\{1,2,3\}'=\{4,5,6\}$

Is the second part where I write $A'=\{1,2,3\}'$ a valid way to write 'complement of set A' ? I say that because I am not sure if we can write $\{1,2,3\}'$ as a substitute to $U-A$. Also note that I am aware of other ways to write it.So my question is mostly just a yes-no one,but any other information you provide will be very much appreciated.

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1 Answer

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Like Christopher Erst, I haven't ever seen $\{1, 2, 3\}'$ used, but since $A = \{1, 2, 3\}$, it follows that $A' = \overline A = A^C = \{1, 2, 3\}'$ is valid, though I wouldn't recommend it.

What I'd suggest is a more direct approach: $A' = \{4, 5, 6\}$ (to show directly that you know what the complement $A' = U - A$ is: writing $A'$ as the set whose members/elements belong to $A'$)?

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