Question

The diagram represents three statements about teachers: p, q, and r.



For how many teachers are both p ∧ r true and q false?

2
4
5
9

Answer 1

I can't see the diagram you mention. Could you upload it or type the numbers shown in each region?

Meanwhile, here is how to get the answer from a 3-circle Venn diagram:

- The teachers for which p ∧ r is true and q is false are exactly those in (p ∩ r) but not in q, i.e. (p ∩ r) ∩ ¬q.
- If the diagram gives the counts:
- let a = number in p ∩ r ∩ ¬q (the part inside p and r but outside q),
- let b = number in p ∩ q ∩ r (the part inside all three).
- then |(p ∧ r) ∧ ¬q| = a (equivalently |p ∩ r| − b).

So find the region inside both p and r but outside q and read its number (or subtract the three-way overlap from the total p∩r). Post the diagram or those numbers and I’ll pick the correct option.