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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: an even number greater than 4
(vi) F: a number not less than 3
Also find A υ B, A ∩ B, B υ C, E ∩ F, D ∩ E, A - C, D - E, E ∩ F, F
Solution:
When a die is thrown, the sample space is given by S = {1, 2, 3, 4, 5, 6}
Accordingly:
(i) A: a number less than 7
A = {1, 2, 3, 4, 5, 6}
(ii) B: a number greater than 7
As S has no element that is greater than 7
B = Φ
(iii) C: a multiple of 3
C = {3, 6}
(iv) D: a number less than 4
D = {1, 2, 3}
(v) E: an even number greater than 4
E = {6}
(vi) F: a number not less than 3
F = {3, 4, 5, 6}
Now,
A υ B = {1, 2, 3, 4, 5, 6}
A ∩ B = Φ
B υ C = {3, 6}
E ∩ F = {6}
D ∩ E = Φ
A - C = {1, 2, 4, 5}
D - E = {1, 2, 3}
F' = S - F = {1, 2}
E ∩ F' = Φ
NCERT Solutions Class 11 Maths Chapter 16 Exercise 16.2 Question 2
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: an even number greater than 4 (vi) F: a number not less than 3. Also find A υ B, A ∩ B, B υ C, E ∩ F, D ∩ E, A - C, D - E, E ∩ F, F
Summary:
(i) A = {1, 2, 3, 4, 5, 6} (ii) B = Φ (iii) {3, 6} (iv) {1, 2, 3} (v) {6} (vi) {3, 4, 5, 6}. Also, A υ B = {1, 2, 3, 4, 5, 6}; A ∩ B = Φ; B υ C = {3, 6}; E ∩ F = {6}; D ∩ E = Φ; A - C = {1, 2, 4, 5}; D - E = {1, 2, 3}; F' = S - F = {1, 2}; E ∩ F' = Φ
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