State true or false: (give reason for your answer)
(i) A and B are mutually exclusive
(ii) A and B are mutually exclusive and exhaustive
(iii) A = BI
(iv) A and C are mutually exclusive
(v) A and BI are mutually exclusive.
(vi) AI, BI, C are mutually exclusive and exhaustive.
1 Answer
Solution :-
(i) A and B are mutually exclusive
So, (A ∩ B) = φ
So, A & B are mutually exclusive.
Hence, the given statement is true.
(ii) A and B are mutually exclusive and exhaustive
A ∩ B = f and A ∪ B = S
Thus, the given statement is true.
(iii) It is observed that
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Thus, the given statement is true.
(iv) It is observed that A ∩ C = {(2, 1), (2, 2), (2, 3), (4, 1)} ≠ φ
A and C are not mutually exclusive.
Thus, the given statement is false.
(v) A ∩ BI = A ∩ A = A
∴ A ∩ BI ≠ φ
A and B’ are not mutually exclusive
(vi) It is observed that A' ∪ B' ∪ C = S
However,
Therefore, events A’, B’ and C are not mutually exclusive and exhaustive.
Thus, the given statement is false.
Answered by Pragya Singh | 1 year agoRelated Questions
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