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

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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Samantha 1 month 2021-08-16T14:39:19+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-08-16T14:40:38+00:00

    \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:

    HOPE IT HELP YOU ✌✌

    0
    2021-08-16T14:41:10+00:00

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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

    ━━━━━━━━━━━━━━━━━━━━━━━━━

    \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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