Answer to Question #185324 in Statistics and Probability for Vaishu

Question

A, B and C are three events. Express the following events in set notations .

(i) simultaneous occurrence of A,B and C.

(ii) occurrence of at least one of them.

(iii) Both A and B occur and C does not occur .

(iv) The event B but not A occur .

(v) Not more than one of the events A,B and C occur .

Answer 1

(i) $A\cap B\cap C$

(ii) $A\cup B\cup C$

(iii) $A\cap B\cap C^c$

(iv) $B\cap A^c$

(v) $[A\cap (B^c\cap C^c)]\cup[B\cap (A^c\cap C^c)]\cup[C\cap (A^c\cap B^c)]$