For the following two question
Let P, Q, and R be logical statements. Use a truth table to prove that_______.
Let P, Q, and R be statement variables, and suppose that the logical expression_______ is false.
The blank is two expressions which I don't know how to type those symbols, hope it doesn't matter.
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$\begingroup$A logical statement like $P$ is meant to be a specific statement. For example, $P$ could mean 'It is raining'.
A statement variable is something we use to indicate that we are dealing with some statement ... but we don't know what it is.
It is like the difference between $2$ and $x$ when doing algebra. The $2$ is a specific number, but the $x$ is some unknown number.
$\endgroup$ $\begingroup$Statement variables are atomic statements, i.e. statements with no connectives in them. Statement variables are usually written as letters $p, q, r, \ldots$.
Logical statements are any statements composed of statement variables and, possibly, connectives. For example: $p$, $\neg p$, $p \land q$, $(q \lor p) \to (r \lor q)$, $\ldots$.
Every statement variable makes for a logical statement, but not every logical statement is a single statement variable.
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