Question

5. If u = (1, 2, 3, 4, ..., 10), A = (1, 2, 3, 4, 5) and B= (1, 3, 5, 7, 9), then find. A^c ii) B^C iii) (AUB) iv) (A intersection B)​

Answer 1

Solution:

Given:

• U = {1, 2, 3, ..., 10}
• A = {1, 2, 3, 4, 5}
• B = {1, 3, 5, 7, 9}

To find:

1. A compliment = A' = ?
2. B compliment = B' = ?
3. A U B = ?
4. A ∩ B = ?

Solution:

1. ‘A compliment’ is the set of elements that are included in Union set but not in set A.

These elements are {6, 7, 8, 9, 10}.

So, Aᶜ = {6, 7, 8, 9, 10}

2. B compliment is the set of numbers included in Union set but not in set B.

These elements are: {2, 4, 6, 8, 10}

So, Bᶜ = {2, 4, 6, 8, 10}

3. ‘A U B’ is the set of numbers which is included in both sets A and B.

These elements are: {1, 2, 3, 4, 5, 7, 9}

Note that the elements should occur only once.

So, A U B = {1, 2, 3, 4, 5, 7, 9}

4. A ∩ B includes set of elements which are common in both sets A and B.

Such elements are: {1, 3, 5}

Hence, A ∩ B = {1, 3, 5}