Respuesta :
Answer:
Step-by-step explanation:
To analyze the information provided and determine the number of students who liked each proposition, you can use a Venn diagram approach. Let's break down the information step by step:
i) 12 liked Proposition 8 and Proposition 13.
ii) 18 liked Proposition 8, but not Proposition 5.
iii) 4 liked Proposition 8, Proposition 13, and Proposition 5.
iv) 25 liked Proposition 8.
v) 15 liked Proposition 13.
vi) 10 liked Proposition 5, but not Proposition 8 nor Proposition 13.
vii) 1 liked Proposition 13 and Proposition 5, but not Proposition 8.
Now, let's calculate the number of students who liked each proposition:
Liked Proposition 8:
From (i), there are 12 students who liked both Proposition 8 and Proposition 13.
From (ii), there are 18 students who liked Proposition 8 but not Proposition 5.
From (iii), there are 4 students who liked all three propositions.
So, the total number of students who liked Proposition 8 is 12 (liked both) + 18 (liked only Proposition 8) + 4 (liked all) = 34 students.
Liked Proposition 13:
From (i), there are 12 students who liked both Proposition 8 and Proposition 13.
From (v), there are 15 students who liked Proposition 13.
From (iii), there are 4 students who liked all three propositions.
From (vii), there is 1 student who liked Proposition 13 and Proposition 5 but not Proposition 8.
So, the total number of students who liked Proposition 13 is 12 (liked both) + 15 (liked only Proposition 13) + 4 (liked all) + 1 (liked Proposition 13 and Proposition 5 only) = 32 students.
Liked Proposition 5:
From (iii), there are 4 students who liked all three propositions.
From (vi), there are 10 students who liked Proposition 5 but not Proposition 8 nor Proposition 13.
From (vii), there is 1 student who liked Proposition 13 and Proposition 5 but not Proposition 8.
So, the total number of students who liked Proposition 5 is 4 (liked all) + 10 (liked only Proposition 5) + 1 (liked Proposition 13 and Proposition 5 only) = 15 students.
Now, you have the number of students who liked each proposition:
Proposition 8: 34 students
Proposition 13: 32 students
Proposition 5: 15 students
