question_answer

Let A, B, C be three mutually independent events. Consider the two statements \[{{S}_{1}}\] and \[{{S}_{2}}\].

\[{{S}_{1}}:A\] and \[B\bigcup C\] are independent

\[{{S}_{2}}:A\] and \[B\bigcap C\] are independent

Then,

A)  Both \[{{S}_{1}}\] and \[{{S}_{2}}\] are true

B)  Only \[{{S}_{1}}\] is true

C)  Only \[{{S}_{2}}\] is true

D)  Neither \[{{S}_{1}}\] nor \[{{S}_{2}}\] is true

E)  None of these