Logic question Truth table

Ace

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So i have to explain this question and im just having a hard time trying to figure it out the question is. If q is true what must be the truth value of the statement qV (q^
~p) which i guess reads out q or( q and not p ).
I know it has to do with constructing a truth table and im trying but i seem to be getting stuck a lot. If anyone can help thank you
 
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So i have to explain this question and im just having a hard time trying to figure it out the question is. If q is true what must be the truth value of the statement
qV (q^
~p) which i guess reads out q or( q and not p ).. I know it has to do with constructing a truth table and im trying but i seem to be getting stuck a lot. If anyone can help thank you

Here it is.
 
Hello, Ace!

If q\displaystyle q is true, what is the truth value of the statement: q(qp)\displaystyle q \vee (q\, \wedge \sim p)

Since q\displaystyle q is true, we consider the two truth values of p.\displaystyle p.

. . \(\displaystyle \begin{array}{cc|cccccc}p&q & q & \vee & (q& \wedge & \sim p) \\ \hline
T&T & T & \color{blue}{T} & T & F & F \\
F&T & T & \color{blue}{T} & T & T & T \\ \hline
&& 1&\color{blue}{3}&1&2&1 \end{array}\)

It is a tautology.
 
Hello, Ace!


Since q\displaystyle q is true, we consider the two truth values of p.\displaystyle p.

. . \(\displaystyle \begin{array}{cc|cccccc}p&q & q & \vee & (q& \wedge & \sim p) \\ \hline
T&T & T & \color{blue}{T} & T & F & F \\
F&T & T & \color{blue}{T} & T & T & T \\ \hline
&& 1&\color{blue}{3}&1&2&1 \end{array}\)

It is a tautology.

Hi can you explain this to me a bit im trying to look up tautology to see if maybe i missed it in class but my math book is super unhelpful right now and so is google
 
Hi can you explain this to me a bit im trying to look up tautology to see if maybe i missed it in class but my math book is super unhelpful right now and so is google
If q is true then [q or (anything)] is true.
If q is false then [q and (anything)] is false and thus {q or [q and (anything)]} is false.

A (simplistic) definition of a tautology is that it is a statement which is true no matter the truth or falsehood of its individual parts. That is, no matter what p and q are, the statement
"{q or [q and (not p)]} has the same truth value as q" is true.

EDIT: Re-writing to make it 'sound' better
 
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