Complement of a set explained

Learn and know the meaning of complement of a set. This is one of the important terms that we can observe while studying set theory. So let us learn what is complement of a set with examples.

Complement of a set explained

Let us consider a universal set U and a set A which is subset of universal set U. then the set of all the elements of universal set which are not elements of set A is called complement of set A. It is represented by A| or Ac. both the notations are correct so any one notation we can use to represent complement of any set.

Let us one example, universal set U = { 1, 5, 7, 9, 10, 12, 13, 15, 16, 17} and a set A = {7, 9, 10, 13} then the complement of set A = {1, 5, 12, 15, 16, 17}.

Representation of Complement of a set through Venn diagram:

Complement of a set explained

The shaded region in the above diagram shows the complement of set A.

Examples:

If set A = {13, 17, 19, 24, 25, 27, 35, 42, 48, 52, 56, 59} and universal set U = {1, 7, 13, 17, 19, 22, 24, 25, 26, 27, 35, 41, 42, 48, 52, 55, 56, 59, 60} then find complement of A.

Solution:

               Given

                              A = {13, 17, 19, 24, 25, 27, 35, 42, 48, 52, 56, 59}

                              U = {1, 7, 13, 17, 19, 22, 24, 25, 26, 27, 35, 41, 42, 48, 52, 55, 56, 59, 60}

Therefore, A| or Ac = {1, 7, 22, 26, 41, 55, 60}

From the given diagram find out complement of B.

Complement of a set explained

From the diagram universal set U = {a, b, c, d, e, f, g, h, i, j} and B = {a, b, c, d}

Therefore, B| = {e, f, g, h, i, j}

Hope that all of you understood the concept complement of a set in detail.

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