In my book it defines "an argument is valid if the premises cannot all be true without the conclusion being true as well."
I had trouble understanding what the author meant ,so I did my best -out of curiosity- to see if I could write that definition in logical form.
This how I tried paraphrase the author's definition of a valid argument:
If the premises are true and the conclusion is true, then the argument is valid, and if the premises are true and conclusion is false, the argument is invalid.
Now here is how I wrote my paraphrase of the author's definition in logical form:
Let P stand for the statement "The premises are true " , C stand for the statement "The conclusion is true", and A stand for the "Argument is valid."
This what my paraphrase in logical form is written:
$[(P\land C)\to A]\land[(P\land\neg C)\to\neg A]$
I do not know if the logical form I created is an accurate representation of what the author wrote as the definition of a valid argument. Do you think it's correct my paraphrase?