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

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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