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I do not quite understand this problem very well as I am constructing truth tables and trying to solve them. Could someone help me explain how you solve this?

The question is as follows...

Consider the statements:

P: $\sqrt{26}$ is irrational
$Q: (27^{\frac13})$ is irrational
$R: \frac{-4}7$ is rational

What are the following statements in words and indicate wether the statement is true or false?

$(P$ and $Q) \implies $$(R)$

$(P$ and $Q)$ $\implies ($not $R)$

$(($not $P)$ and $Q)$ $\implies $$R$

$(P$ or $Q) \implies ($not $R)$

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    (P and Q) then R is True (P and Q) => (not R) is True ((not P) and Q) => R is False (P or Q) => (not R) is False – 2017-02-09
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    What can you say about $P$, $Q$, and $R$? Which ones are true? – 2017-02-09
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    P and R are true, Q is false? – 2017-02-09
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    Correct! So, what's the truth value of $P \wedge Q$? – 2017-02-09
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    So.... False, False, False, False? – 2017-02-09
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    If $P$ is true and $Q$ is false, then $(P\text{ and }Q)$ is false, so $(P\text{ and }Q)\implies R$ is false. – 2017-02-09
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    No, remember that $A \rightarrow B$ is false only when $A$ is true and $B$ is false. I didn't see you first comment in its complete form (you submitted it early and it was still incomplete). So, I didn't mean to suggest it was wrong. I'll look at it now. – 2017-02-09
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    Ah, okay thank you! – 2017-02-09
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    OK. I looked at it and you got three out of four right. Remember, if $A$ is false, then $A \rightarrow B$ is true. – 2017-02-09
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    True, True, True, False! – 2017-02-09
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    Yes. That's it! Implications with false antecedents are counterintuitive at first. This exercise is meant to familiarize who solves it with how they work. – 2017-02-09

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