Question

In a single throw of a die describe the event:

F = Getting a number not less than 3.
Also, find A ∪ B, A ∩ B, B ∩ C, E ∩ F, D ∩ F and \[ \bar { F } \] . 

 

Answer 1

When a dice is thrown, the sample space is given by S = {1, 2, 3, 4, 5, 6}.
Accordingly, we have:

 F = {3, 4, 5, 6}

Here, A = {1, 2, 3, 4, 5, 6} and B = Φ
∴ A ∪ B = {1, 2, 3, 4, 5, 6}

Here, A = {1, 2, 3, 4, 5, 6}  and B = Φ
∴ A ∩ B = Φ

Here, B = Φ and C = {3, 6}
∴ B ∩ C = Φ

Here, E = {6}  and F = {3, 4, 5, 6}
∴ E ∩ F = {6}

Here, D = {1, 2, 3}  and F = {3, 4, 5, 6}
∴ D ∩ F = {3}

Here, F = {3, 4, 5, 6} and S = {1, 2, 3, 4, 5, 6}

∴ \[\bar{F} = S - F = {1, 2}\]