Definition Of The Complement Of A Set

Thread starter Bashyboy
Start date Oct 5, 2012
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In summary, the complement of a set is the set of all elements that are not contained in the original set. It is denoted as A<sup>c</sup> or A<sup>'</sup> and has a mutually exclusive relationship with the original set. The complement of a set can be determined by listing the elements not in the original set or by subtracting the original set from the universal set. For example, the complement of the set of vowels (A, E, I, O, U) in the universal set of all letters in the alphabet would be all the consonants (B, C, D, F, G, H, J, K, L, M, N, P, Q, R,

Oct 5, 2012

Bashyboy

Hello, my book defines the complement of a set like so: {x ∈ U | x /∈ A}

To me, it seems like the definition should be [itex](x| x \in U \wedge x \notin A)[/itex]

Which is more proper?

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Oct 5, 2012

HallsofIvy

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They both say exactly the same thing.

Oct 5, 2012

Bashyboy

Okay, thank you.

What is the complement of a set?

The complement of a set is the set of all elements that are not contained in the original set. In other words, it includes all the elements that are outside of the original set.

How is the complement of a set denoted?

The complement of a set A is denoted as A^c or A^'.

What is the relationship between a set and its complement?

The complement of a set is the set of all elements that are not included in the original set. Therefore, the elements in the complement are mutually exclusive from the elements in the original set. This means that if an element is in the original set, it cannot be in the complement, and vice versa.

How is the complement of a set determined?

To find the complement of a set, you can simply list all the elements that are not in the original set. Alternatively, you can use the universal set, which is the set of all possible elements, and subtract the original set from it to get the complement.

What is an example of finding the complement of a set?

Let's say the universal set is the set of all letters in the alphabet, and the original set is the set of vowels (A, E, I, O, U). The complement of this set would be all the letters in the alphabet that are not vowels, which would be B, C, D, F, G, H, J, K, L, M, N, P, Q, R, S, T, V, W, X, Y, Z.