Answer:
a.) only E occurs :
E((FUG)')
b.) both E and G but not F
EG(F')
C.) Atleast one of the events :
(E U G U F)
d.) Atleast two of the events
(EG U EF U GF)
E.) all three occurs
(EGF)
F.) none of the events occur :
(E U G U F)'
G.) At most one of the events occur
(EG U EF U GF)'
H.) at most two of them occur
(E' U G' U F')
I.) exactly two of them occur;
(EG U EF U GF) * (EGF)'
j. at most three of them occur.
EFG U (EFG)'
Step-by-step explanation:
Events = {E, F, G}
a.) only E occurs :
E((FUG)') ; E and not F or G
b.) both E and G but not F
EG(F') ; both E and G and not F
C.) Atleast one of the events :
(E U G U F) ; Either E or F or G
d.) Atleast two of the events
(EG U EF U GF) ; Either EG or EF or GF occurs
E.) all three occurs
(EGF) ; All three events, E, G and F occurs
F.) none of the events occur :
(E U G U F)' ; Neither E, G nor F occurs
G.) At most one of the events occur
(EG U EF U GF)' ; complement of atleast two) at most one
H.) at most two of them occur
(E' U G' U F') ; Either E , F or G does not occur
I.) exactly two of them occur;
(EG U EF U GF) * (EGF)' ; Exactly two events occurs and all three events Do not occur
j. at most three of them occur.
EFG U (EFG)' ; All three events occur union all three events do not occur
and 
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