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 = B^{I}

**(iv)** A and C are mutually exclusive

**(v) **A and B^{I} are mutually exclusive.

**(vi)** A^{I}, B^{I}, C are mutually exclusive and exhaustive.

Asked by Abhisek | 1 year ago | 126

**(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

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 ∩ B^{I} = A ∩ A = A

∴ A ∩ B^{I} ≠ 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.

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