Question

Find AUB,AnB,A-B and B-A for the following sets A=(a,b,c,e,u) and B =( a,e,i,o,u)​

Answer 1

Answer:

• A U B = { a, b, c, e, i, o, u }
• A ∩ B = { a, e, u }
• A - B = { b, c }
• B - A = { i, o }

Solution:

Given that,

• A = { a, b, c, e, u }
• B = { a, e, i, o, u }

Find A U B

We know, A U B represents the union of two sets, where the resultant set will contain elements from both sets A and B.

So,

> A U B = { a, b, c, e, u } U { a, e, i, o, u }

Because, a set doest not contain duplicate values so wel will exclude the elements of B which are already present in A.

> A U B = { a, b, c, e, i, o, u }

Find A ∩ B

This is an intersection operator which gives a set which has elements that are in both the sets A and B if there are no common elements then this would give a null set.

> A ∩ B = { a, b, c, e, u } ∩ { a, e, i, o, u }

We can clearly see that there are only 3 common elements (a, e, u) in the sets A and B.

> A ∩ B = { a, e, u }

Find A - B

Two sets A and B if subtracted then it would give a set that has only elements of A and It won't contain any elements with the set B, represented by A - B.

Here, A - B gives a set that has only elements of A. Let's find it out.

> A - B = { a, b, c, e, u } - { a, e, i, o, u }

We can see that there are 2 elements (b, c) that are only present in set A. Hence,

> A - B = { b, c }

Find B - A

The definition defined remains the same. Here, this operation will give a set that elements of only B and It won't contain any common elements with the set A.

> B - A = { a, e, i, o, u } - { a, b, c, e, u }

Here, we can see that there are 2 elements (i, o) which are only present in set B. So,

> B - A = { i, o }

Answer 2

Question:-

Find AUB,A∩B,A – B and B – A for the following sets A = {a,b,c,e,u} and B = {a,e,i,o,u}.

Given:-

• A = {a,b,c,e,u}.
• B = {a,e,i,o,u}.

To Find:-

• AUB,
• A∩B,
• A – B,
• B – A.

Solution:-

AUB = {a,b,c,e,u} U {a,e,i,o,u}

AUB = {a,b,c,e,i,o,u}.

A∩B = {a,b,c,e,u} ∩ {a,e,i,o,u}

A∩B = {a,e,u}.

A – B = {a,b,c,e,u} – {a,e,i,o,u}

A – B = {b,c}.

B – A = {a,b,c,e,u} – {a,e,i,o,u}

B – A = {i,o}.

Answer:-

• AUB = {a,b,c,e,i,o,u}.
• A∩B = {a,e,u}.
• A – B = {b,c}.
• B – A = {i,o}.

More Information:-

• ∪ = The set made by combining the elements of two sets. So the union of sets A and B is the set of elements in A, or B, or both. The symbol is a special "U" like this: ∪.

• ∩ = The symbol we use for the intersection is ∩. The word that you will often see that indicates an intersection is "and". Find A∩B.

• A – B and B – A = A-B is the set of all elements that are in A but NOT in B, and B-A is the set of all elements that are in B but NOT in A. Notice that A-B is always a subset of A and B-A is always a subset of B.