Question

The diagram represents three statements: p, q, and r. For what value is both p ∧ r true and q false?

2
4
5
9

Answer 1

The correct option is 4. For value 9 both p ∧ r true and q false.

Explanation:

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

We need to find the value for which p ∧ r is true and q false.

p ∧ r true mean the intersection of statement p and r. It other words p ∧ r true means p is true and r is also true.

From the given venn diagram it is clear that the intersection of p and r is

`p\cap r=9+2=11`

p ∧ r true and q false means intersection of p and r but q is not included.

From the given figure it is clear that for value 2 all three statements are true. So, the value for which both p ∧ r true and q false is

`11-2=9`

Therefore the correct option is 4.

Answer 2

9

Explanation:

From the diagram:

• only p true in 8 cases;
• only q true in 7 cases;
• only r true in 6 cases;
• both p and q true, r false in 5 cases;
• both p and r true, q false in 9 cases;
• both q and r true, p false in 4 cases;
• all three p, q and r true in 2 cases.

So, correct option is 9 cases.