Answer
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Step 1:: The event that both E and F occur.
In set notation, this is represented as the intersection of events E and F, which is expressed as E ∩ F.
Step 2:: The event that E or F occurs.
In set notation, this is represented as the union of events E and F, which is expressed as E ∪ F.
Step 3:: The event that both E and F occur but G does not occur.
In set notation, this is represented as the intersection of events E and F, intersected with the complement of event G, which is expressed as (E ∩ F) ∩ G^c.
Step 4:: The event that neither E nor F occurs but G does occur.
In set notation, this is represented as the intersection of the complements of events E and F, intersected with event G, which is expressed as (E^c ∩ F^c) ∩ G.
Final Answer
a. (E ∪ F)^c ∩ G: This option does not represent the correct set notation since it represents the event that G does not occur and either E or F does not occur. b. (E ∩ F)^c ∪ G: This option does not represent the correct set notation since it represents the event that at least one of E, F, or G does not occur. c. (E^c ∪ F^c) ∩ G: This option correctly represents the set notation for the event that neither E nor F occurs but G does occur. d. (E^c ∪ F^c)^c ∩ G: This option does not represent the correct set notation since it represents the event that at least one of E or F must occur and G does occur. e. None of the above: This is the correct answer as none of the given options correctly represent the set notation for the event that neither E nor F occurs but G does occur.
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