Question

A die is thrown. Describe the following events:

1. A: a number less than 7
2. B: a number greater than 7
3. C: a multiple of 3
4. D: a number less than 4
5. E: an even number greater than 4
6. F: a number not less than 3

Also find A ∪ B, A ∩ B, B ∪ C, E ∩ F, D ∩ E, A – C, D – E, E ∩ F', F'

Answer 1

S = {1, 2, 3, 4, 5, 6}
i. a number is less than 7 = {1, 2, 3, 4, 5, 6}

ii. B: a number is greater than 7 = No number in the dice is greater than 7

= ϕ

iii. C: a number is multiple of 3 = {3, 6}

iv. D: a number is less than 4 = {1, 2, 3}

v. E: a number is even greater than 4 = {6}

vi. F = a number is not less than 3 = {3, 4, 5, 6}

Now A ∪ B = {1, 2, 3, 4, 5, 6} ∪ ϕ

= {1, 2, 3, 4, 5, 6}

A ∩ B= {1, 2, 3, 4, 5, 6} ∩ ϕ

= ϕ

B ∪ C = ϕ ∪ {3, 6} = {3, 6}

E ∪ F = {6} ∪ {3, 4, 5, 6} = {3, 4, 5, 6}

D ∩ E = {1, 2, 3} ∩ {6}

A – C = {1, 2, 3, 4, 5, 6} – {3, 6}

= {1, 2, 4, 5}

F’ = {3, 4, 5, 6}’ = S – {3, 4, 5, 6}

= {1, 2, 3, 4, 5, 6} – {3, 4, 5, 6}

= {1, 2}

E ∩ F’ = {6} ∩ {3, 4, 5, 6}’

= {6} ∩ {1, 2} = ϕ