question_answer

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