I'm a modern philosophy student and I'm reading content on the truth-value of sentences in logical structure, but I had trouble underatanding how connectives contribute to the truth-values of say sentences represented as 'p' and 'q'. I know that if q is True, then it supposes that p is also true, since p refers to q. Next it introduced the idea of connectives as truth-value functions to the sentences 'p' and 'q', here was suppose to be photos attached to this, but the option is not available to me as of this moment, so let me try to explain the table as best I can: say there are three seperate columns labled 'p' '&' and 'q' and under each them, there are a set of values of either T(truth) or F(false). For every single set of T or F values there exists a row to set the apart from the other set of T and F values: For the first there is TTT (p=T; &=T, p=T); the next row says FFT (p=F; &=F, p=T); the third row says TFF (p=T; &=F, p=F); and the last says FFF (p=F; &=F, p=F); the book later explains this:
Consider the connective & (and). We could assign to this the following function: p & q has the value true, if p has value true and q has value true. Otherwise it has the value false. Sometimes this is represented in a truth-table as follows: The middle column represents the value that must be assigned to p & q, when p and q each has the value given in the columns beneath the symbols ‘p’ and ‘q’."
What do the other set of values of T and F mean?
true and falseequal tofalse?" or both, or something else entirely.