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Chapter 2: Q31 (page 35)

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

Expert verified

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

Step by step solution

01

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”.

02

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”.

03

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”.

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