We want to find the logic statements that represent the given Ven Diagrams.
1) p ∪ r
2) q ∩ r.
3) r ∪ (p ∩ q).
Let's analyze each one of the graphs:
1) We can see that we have p and r completely shaded (and the only region of q that is shaded is the one that belongs to r or p).
Then this is just the union of sets p and r.
This is written as:
p ∪ r
2) Here we can see that the shaded region is the intersection between q and r. (where intersection means the set of all the common elements between q and r).
The intersection between two sets is written as:
q ∩ r.
3) Here we have a combination of the two previous ones.
We have the union between intersection between p and q, and the complete r set.
Then this is written as:
r ∪ (p ∩ q).
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