Question

Let U={1,2,3,4,5,6},A={2,3} and B={3,4,5} find A dash and B dash and A intersection B​

Answer 1

Answer:

Let U = {1, 2, 3, 4, 5, 6}, A = {2, 3} and B = {3, 4, 5}.

Find A′, B′ , A′ ∩ B′, A ∪ B and hence show that ( A ∪ B )′ = A′∩ B′.

Solution:

U = {1,2,3,4,5,6} , A={2,3} and B={3,4,5}

So,

A'= {1,4,5,6}

B' ={1,2,6}

A′ ∩ B′ = {1,6}

Now we have to represent that:

( A ∪ B )′ = A′∩ B′.

First of all we have to find that:

f( A ∪ B )

(A U B) = {2,3,4,5,6}

So,

(A ∪ B)′ = {1,6}

We know, A′ ∩ B′ = {1,6}

So,

Hence,

(A ∪ B)′ = A′∩ B′

\rule{300}{3.5}

Extra Information:

★ Set:

A set is a collectionof objects that are clearly identified. The objects in the set are called member & elements of the set. Each member is said to belong to the set. The symbol ∈ is used to denote belongs to or is an element of or is a member of.

★ Complement of a set:

If a set A is a subset of a given Universal Set (U), then the differnce set U/A is the complement of A.

We write it as: U/A = A' , We say: A complement.

★ Universal set:

When a given set is overall set to which all the objects in a discussion belong, the given set is called the Universal Set.

We write is as: U, We say : Universal set.

★ Union of Sets:

The set which consits of all the elements that belong to A together with all the members of B is {0, 1, 3, 5, 7, 9} It is called the Union of A and B.

We can write is as : A ∪ B.