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I have a trouble on this. If someone helps, it would be great.

$p\wedge q = 1$ and $q^ı\vee r^ı = 0$

What is the truth value of this respectively?

My answer:

$1,0,1$

Fiv
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1 Answers1

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The condition

$$ p \wedge q = 1 $$

implies that $p = 1$ and $q = 1$. This means that

$$ q^\prime \vee r^\prime = 0 \vee r^\prime = r^\prime = 0$$

From the above we conclude $r = 1$. Thus $\{p,q,r\} = \{1,1,1\}$

David
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    You can also use the rule of de Morgan : $q'\ or\ r'=(q\ and\ r)'$. This gives $q\ and\ r=1$ and therefore $q=1$ and $r=1$ – Peter Sep 19 '17 at 18:48
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    Yes, as @Peter points out, de Morgan's rule will also work. If you will be studying logic then de Morgan's rules are very helpful. – David Sep 19 '17 at 18:52
  • Thanks a lot for your great answer! If you show the rule of de Morgan (or someone) i'd be happy. – Fiv Sep 19 '17 at 19:14
  • Can someone solve this question with de Morgan's rule? – Fiv Sep 20 '17 at 13:49