Question

Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} be the universal set and let A = {2, 3, 4, 5, 6} and B = {3, 5, 7, 8} be
its subset.
Find:

(i) A’ U B’ (ii) A’ Ո B’​

Answer 1

1.{1,2,4,6,7,8,9,10}

2.{1,9,10}

Hope it helped,please do cross check my answer.

Answer 2

Given :-

• Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} be the universal set and let A = {2, 3, 4, 5, 6} and B = {3, 5, 7, 8} be its subset.

To find :-

• Value of A’ U B’
• Value of A’ Ո B’

Solution :-

• Universal set

→ A set that contains all sets in a given context is called universal set

→ It is denoted by " U "

• Union of sets

→ The union of A and B is the set of all those element which belong either A or to B or to both A and B is known as union of sets

→ It is denoted by " A U B " (read as A union B)

• Intersection of sets

→ The intersections of A and B is a set of all those elements that belongs to both A and B is known as intersection of sets

→ It is denoted by " A Ո B " (read as A intersection B)

• Complement set

→ The complement of a subset of universal set U is the set of all elements of its which are not the element of A

→ It is denoted by A'

Now, it is given that

• U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

• A = {2, 3, 4, 5, 6}

• B = {3, 5, 7, 8}

According to first question

→ A’ U B’

To solve this firstly we have to find out complement of A then after complement of B

→ A' = {1, 7, 8, 9, 10}

→ B' = {1, 2, 4, 6, 9, 10}

So,

→ A’ U B’ = {1, 2, 4, 6, 7, 8, 9, 10}

• Note : U → This shows union of set

According to second question

→ A’ Ո B’

To solve this firstly we have to find out complement of A then after complement of B

→ A' = {1, 7, 8, 9, 10}

→ B' = {1, 2, 4, 6, 9, 10}

So,

→ A’ Ո B’ = {1, 9, 10}

• Note : Ո → This shows intersection of set