Given: A dice is thrown once. 

To Find: Find the given events, and also find the Also, find A ∪ B, A ∩ B, B ∩ C, E ∩ F, D ∩ F and \(\bar{F}\)

Explanation: In a single throw of a die, the possible events are: 

S = {1, 2, 3, 4, 5, 6} 

Now, According to the subparts of the question, we have certain events as: 

(i) A = getting a number below 7 

So, The sample spaces for A are: 

A = {1, 2, 3, 4, 5, 6} 

(ii) B = Getting a number greater than 7 

So, the sample spaces for B are: 

B = {Փ} 

(iii) C = Getting multiple of 3 

So, The Sample space of C is 

C = {3, 6} 

(iv) D = Getting a number less than 4 

So, The sample space for D is 

D = {1, 2, 3}

(v) E = Getting an even number greater than 4. 

The sample space for E is 

E = {6} 

(vi) F = Getting a number not less than 3. 

The sample space for F is 

⇒ F = {3, 4, 5, 6} 

Now, 

A = {1, 2, 3, 4, 5, 6} and B = {Փ}

⇒ A∪B = {1, 2, 3, 4, 5, 6}

A = {1, 2, 3, 4, 5, 6} and B = {Փ}

⇒ A∩B = {ϕ}

B = {Փ} and C = {3, 6}

⇒ B∩D = {ϕ}

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

⇒ E∩F = {6}

E = {6} and D = {1, 2, 3}

⇒ D∩F = {3}

And, For \(\bar{F}\) = S - F

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

⇒ \(\bar{F}\) = {1,2}

Hence, These are the events for given ecperiment