Write the expression (p^ ~q) ^ r, using only the operators v and ~.
The question meant the ^ operator with v operator?
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hm so if i get this right, ^ means AND, v means OR and ~ means negation. Does that solve your problem? – amakelov Jun 24 '16 at 14:49
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is it replace the operator ^ with v operator? – sudl Jun 24 '16 at 14:52
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1the question is asking you to rewrite the logical expression (p AND (NOT q)) AND r using only the operations OR and NOT – amakelov Jun 24 '16 at 14:53
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No, we can not just replace the $\wedge$ with a $\vee$. This would be wrong because they are not the same thing.
We have: $$(p \wedge \sim q) \wedge r$$ We need to convert this to OR and NOT somehow. Conversions between AND and OR are done with De Morgan's Law: $$\sim (u \wedge v) \iff \sim u \vee \sim v$$ Using this, we can take the negation of both sides to find that: $$u \wedge v \iff \sim (\sim u \vee \sim v)$$ Now, where ever you see a $\wedge$, you can use this formula by substituting the appropriate $u$ and $v$ to convert the expression into something with only $\sim$ and $\vee$. Good luck!
Noble Mushtak
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Hint: $(p \wedge \neg q) \wedge r = \neg (\neg((p \wedge \neg q) \wedge r))$. It's all De Morgan's laws from there.
P.S. Since I'm going to guess you don't know De Morgan's laws, there is a master mathematician who know's just about everything. His name is Google.
Dane Bouchie
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