Here we will turn to a more detailed study of
arguments like those we encountered in the previous topic. Our
study will be much more comprehensive. In particular, we shall
develop a system that is complete in that it enables one to
answer any question regarding the validity of arguments involving
our conditionals (if p then q sentences) and such terms as "and,"
"or," "not," and "if and only if." We recommend that you do the
flash tutorials for a section before proceeding to the exercises
if you are just starting.
If you simply wish to construct or check some truth tables go to the Truth Table Builder
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Section 1: Our Formal Language Initially we introduced the notion of a
sentence of our language. With only a bit of practice you should
not have much trouble in distinguishing those strings of symbols
that are sentences from those that are not.
We then turned to a study of sentential forms and substitution instances. Practice should enable you to work with these without difficulty. We relate actual statements to our formal language by way of symbolizing them. So we shall look at some examples of putting sentences into our formal language. Recall that the capital letters stand for the unnegated statements. And recall as well that is generally best to work from 'the outside in'. |
Section 2: Truth Tables and their Use (including the Truth Table Builder) When we symbolized we worked from the
'outside in', but when we do truth-tables we work from the
'inside out'. For example, suppose `P' receives the value T, `Q'
receives the value F, and `R' receives the value F. Let us look
at: (P ‹-› ~Q) & (R v ~Q) The sentence as a whole
is a conjunction, but in order to know what value it receives we
have to know the value that the conjuncts receive. The left
conjunct receives a T since it is a biconditional and 'P' and
'~Q' both receive a T. The right conjunct receives a T since it
is a disjunction and '~Q' receives a T. So our whole sentence
receives a T. |