The Venn diagram reveals that 35 students exclusively enjoy outdoor games, while 34 students engage in both video games and indoor activities, excluding outdoor games.
Let's use a Venn diagram to represent the information given:
Let:
V represent the set of students who like to play video games,
I represent the set of students who like to play indoor games,
O represent the set of students who like to play outdoor games.
Now, we can fill in the values based on the given information:
The number of students who like to play video games (V) is 60.
The number of students who like to play indoor games (I) is 70.
The number of students who like to play outdoor games (O) is 75.
The number of students who play both indoor and outdoor games (I ∩ O) is 30.
The number of students who play video games and outdoor games (V ∩ O) is 18.
The number of students who play video games and indoor games (V ∩ I) is 42.
The number of students who play all types of games (V ∩ I ∩ O) is 8.
Now, let's find the values for the regions in the Venn diagram:
(i) Students who play only outdoor games:
n(O only) = n(O) - n(I ∩ O) - n(V ∩ O) + n(V ∩ I ∩ O)
n(O only) = 75 - 30 - 18 + 8 = 35
(ii) Students who play video games and indoor games, but not outdoor games:
n(V ∩ I only) = n(V ∩ I) - n(V ∩ I ∩ O)
n(V ∩ I only) = 42 - 8 = 34
So, according to the Venn diagram:
(i) There are 35 students who play only outdoor games.
(ii) There are 34 students who play video games and indoor games, but not outdoor games.