Refer to question 6 above, 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’

(iv) A and C are mutually exclusive

(v) A and B’ are mutually exclusive.

(vi) A’, B’, C are mutually exclusive and exhaustive.

since 2 dice are thrown the sample space will consist of following outcomes

Here

And

(i) A and B are mutually exclusive (A ∩ B) = ϕ

Since A and B has no common element,

So, A & B are mutually exclusive.

Thus, the given statement is true.

(ii) A and B are mutually exclusive and exhaustive

A ∪ B = = S

⇒ A ∪ B = S

And from (i) we have A and b are mutually exclusive

∴ A and B are mutually exclusive and exhaustive.

So, the statement is true.

(iii) A = B

Thus, the statement is true.

(iv) A and C are mutually exclusive

Here A ∩ C = ≠ ϕ

Since A and C have common element,

So, they are not mutually exclusive

So, the given statement is false.

(v) A and B’ are mutually exclusive.

A ∩ B’ = A ∩ A = A

∴ A ∩ B’ ≠ ϕ

So, A and B’ not mutually exclusive.

Hence, the given statement is false.

(vi) A’, B’, C are mutually exclusive and exhaustive.

Here A’ =

B=

And