Solving Set Complement

Introduction to solving set complement

Let `xi` be the universal set. Let A be a set in `xi` . Then the complement of the set A is the set of all elements in U that doesnot belong to A. The complement of the set A is denoted by A’ or A c.

For example: Let `xi` = {1, 2, 3, 4, 5} and A = {1, 2}

Then A’ = {3, 4, 5}. Here we have taken the values of `xi` that doesn’t belong to A.

Using the complement concept, the important law known as De Morgan’s laws is given by:

1. (AUB)’ = A’∩ B’

2. (A ∩ B)’ = A’UB’

Now let us see few problems on this topic solving set complement. I like to share this Complement of a Set with you all through my article.

Example Problems on Solving Set Complement.

Ex 1: Let `xi` = {0, 1, 2, 3, 4, 5, 6}. Let A = {0, 1, 2, 3} and B = {3, 4, 5, 6}. Find A’UB’

Soln: Given: A = {0, 1, 2, 4,5, 6} `=>` A’ = {4, 5, 6}

B = {3, 4,5, 6} `=>` B’ = {0, 1, 2}

Therefore A’UB’ = {0, 1, 2, 4, 5, 6}

Ex 2: Let `xi` = {a, b, c, d, e, f} Let A = {a, b, d}

Let B = {b, c, d, e, f}. Find A’∩ B’.

Soln: Given: A = {a, b, d} `=>` A’ = {c, e, f}

B = {b, c, d, e, f} `=>` B’ = {a}

Therefore A’∩ B’ = { } [Empty set]

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More Example Problems on Solving Set Complement.

Ex 3: Let `xi` = {p, q, r, s, t, u, v}. Let A = {p, r, t, v} and B = {p, q, r, s}. Find (A’∩ B’)’

Soln: Given: A = { p, r, t, v} `=>` A’ = {q, s, u}

B = { p, q, r, s} `=>` B’ = {t, u, v}

A’ U B’ = {q, s, t, u, v}

Therefore (A’ U B’)’ = {p, r} [Here only p and r are not an element of A’UB’]

Ex 4: Let`xi` = {1, 2, 3, 4, 5, 6, 7}.Let = {1, 3, 5, 7}

and Y= {2, 4, 6, 7}. Find (‘X’∩ Y’)’

Soln: Given: X = {1, 3, 5, 7} `=>` X’ = {2, 4, 6}

Y = {2, 4, 6, 7} `=>` Y’ = { 1, 3, 5}

Therefore X’∩ Y’ = { } [Empty set]

Therefore (X’∩ Y’)’ = {1, 2, 3, 4, 5, 6, 7} [Empty set (`O/` )complement is the universal set (`xi` )and vice versa]