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

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