Question

A die is thrown. Describe the following events:
(i) \(A: a\) number less than \(7\)
(ii) \(B: a\) number greater than \(7\)
(iii) \(C: a\) multiple of \(3\)

(iv) \(D: a\) number less than \(4\)
(v) \(E: a\) even number greater than \(4\)
(vi) \(F: a\) 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

Sample Space:

When a die is thrown,
S = {1, 2, 3, 4, 5, 6}

---

Description of Events:

A: A number less than 7
A = {1, 2, 3, 4, 5, 6}

B: A number greater than 7
B = ∅

C: A multiple of 3
C = {3, 6}

D: A number less than 4
D = {1, 2, 3}

E: An even number greater than 4
E = {6}

F: A number not less than 3
F = {3, 4, 5, 6}

---

Required Set Operations:

A ∪ B = {1, 2, 3, 4, 5, 6}

A ∩ B = ∅

B ∪ C = {3, 6}

E ∩ F = {6}

D ∩ E = ∅

A − C = {1, 2, 4, 5}

D − E = {1, 2, 3}

F' = S − F = {1, 2}

E ∩ F' = ∅

---

Final Answer:

All events and required set operations have been described using the sample space of the die.