Question

What can you conclude if the following sentences are all true?

1. If(1) p, then q.
2. (2) p
3. I(3) q, then not r.

(4) s or r

Short answer

From the given statements, it can be concluded that “s is true”.

Step-by-step solution

Step 1. Relation between statements 1 and 2.

All the statements,

if p then q;

p;

if q then not r;

s or r; is true.

So, the second statement “p is true” implies that q is true from the first statement since the first statement is “if p then q”, therefore, “p is true so q is true”.

Step 2. Relation between statements 2 and 3.

Since q is true, therefore, r is not true because statement 3 is “if q then not r”.

Step 3. Relation between statements 3 and 4.

Lastly from the fourth statement “r is false but s is true” because statement 4 is “s or r”. Therefore, the possible conclusion that can be drawn from all these is that “s is true”.