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: an 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 ∩ FI, FI
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Answer 1

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$\Large\fbox{\color{purple}{QUESTION}}$

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: an 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 ∩ FI, FI

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$\bf\Huge\red{\mid{\overline{\underline{ ANSWER }}}\mid }$

➡️Let us assume that 1, 2, 3, 4, 5 and 6 are the possible out comes when the

die is thrown.

➡️So, S = (1, 2, 3, 4, 5, 6)

➡️As per the conditions given in the question,

➡️(i) A: a number less than 7

➡️All the numbers in the die are less than 7,

All the numbers in the die are less than 7,A = (1, 2, 3, 4, 5, 6)

➡️(ii) B: a number greater than 7

➡️There is no number greater than 7 on the die

➡️Then,

➡️B= (φ)

➡️(iii) C: a multiple of 3

➡️There are only two numbers which are multiple of 3.

➡️Then,

➡️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)

➡️Also we have to find, A U B, A ∩ B, B U C, E ∩ F, D ∩ E, D – E, A – C, E ∩ F’, F’

➡️So,

➡️A ∩ B = (1, 2, 3, 4, 5, 6) ∩ (φ)

➡️= (φ)

➡️B U C = (φ) U (3, 6)

➡️= (3, 6)

➡️E ∩ F = (6) ∩ (3, 4, 5, 6)

➡️= (6)

➡️D ∩ E = (1, 2, 3) ∩ (6)

➡️= (φ)

➡️D – E = (1, 2, 3) – (6)

➡️= (1, 2, 3)

➡️A – C = (1, 2, 3, 4, 5, 6) –  (3, 6)

➡️= (1, 2, 4, 5)

➡️F’ = S – F

➡️= (1, 2, 3, 4, 5, 6) – (3, 4, 5, 6)

➡️= (1, 2)

➡️E ∩ F’ = (6) ∩ (1, 2)

➡️= (φ)

$\Large\mathcal\green{FOLLOW \: ME}$

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Answer 2

$\huge\purple\star\underline\mathfrak\pink{</em></strong><strong><em>ANSW</em></strong><strong><em>ER</em></strong><strong><em> :-}\purple\star$

➡️Let us assume that 1, 2, 3, 4, 5 and 6 are the possible out comes when the die is thrown.

➡️So, S = (1, 2, 3, 4, 5, 6)

➡️As per the conditions given in the question,

➡️(i) A: a number less than 7

➡️All the numbers in the die are less than 7,

All the numbers in the die are less than 7,A = (1, 2, 3, 4, 5, 6)✔

➡️(ii) B: a number greater than 7

➡️There is no number greater than 7 on the die

➡️Then,

➡️B= (φ)✔

➡️(iii) C: a multiple of 3

➡️There are only two numbers which are multiple of 3.

➡️Then,

➡️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)✔

➡️Also we have to find, A U B, A ∩ B, B U C, E ∩ F, D ∩ E, D – E, A – C, E ∩ F’, F’

➡️So,

➡️A ∩ B = (1, 2, 3, 4, 5, 6) ∩ (φ)

➡️= (φ)✔

➡️B U C = (φ) U (3, 6)

➡️= (3, 6)✔

➡️E ∩ F = (6) ∩ (3, 4, 5, 6)

➡️= (6)✔

➡️D ∩ E = (1, 2, 3) ∩ (6)

➡️= (φ)✔

➡️D – E = (1, 2, 3) – (6)

➡️= (1, 2, 3)✔

➡️A – C = (1, 2, 3, 4, 5, 6) – (3, 6)

➡️= (1, 2, 4, 5)✔

➡️F’ = S – F

➡️= (1, 2, 3, 4, 5, 6) – (3, 4, 5, 6)

➡️= (1, 2)✔

➡️E ∩ F’ = (6) ∩ (1, 2)

➡️= (φ)✔

Step-by-step explanation:

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