Sentential Connectives and Truth Tables
In Sentential, instead we talk of 'connectives', and these are used to construct sentences that are non-basic.
Here is a quick run-down of what you are likely to encounter in terms of connectives:
The '&' symbol, this signifies conjunction. For instance, if A means 'it is Autumn' and B means 'it is hot', then 'A & B' is 'it is Autumn and it is hot'.
Next, comes along the '¬' symbol; this is used to illustrate negation, one of the easiest to understand - so ¬A is 'it is not Autumn'.
Where you think of 'or' then in sentential you should think "disjunction" and this is shown through the v sign, like this:
A v B - 'it is Autumn or it is hot'.
It is very useful to be able to use the conditional so we can show that one thing if another, and this is done with the sideways horseshoe connective, however as this is not easily reproduced here we will use -> instead.
So A -> B means 'if it is Autumn then it is hot'
Finally, there is the equivalence connective which you will probably see less often, and uses the 'if and only if' symbol common in maths; here we use <->
So A <-> B means 'It is Autumn if and only if it is hot'.
Truth Tables
Truth tables show the inputs to a connective and then what the output is. For instance, the truth table for '&' is as follows:
P Q P&Q
--------------------
T T T
T F F
F T F
F F F
Here we can clearly see therefore that proposition P & Q is only true in the precise circumstance where both of P and Q are individually true, in all other circumstance it is false.
As a starter exercise in sentential logic, now create the truth tables for the other connectives above.
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