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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 鈥�s is true鈥�.

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 鈥�p is true鈥� implies that q is true from the first statement since the first statement is 鈥渋f p then q鈥�, therefore, 鈥�p is true so q is true鈥�.

02

Step 2. Relation between statements 2 and 3.

Since q is true, therefore, r is not true because statement 3 is 鈥渋f q then not r鈥�.

03

Step 3. Relation between statements 3 and 4.

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

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Most popular questions from this chapter

Cut the Mobius band lengthwise down the middle. (Start at a point midway between the edges and cut around the band.) What is the result? Cut the band a second time down the middle. Write a sentence or two describing what happens.

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The figure:

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