Please help with this question, my English is not that good:
Here is a truth table for the new symbol *
P * Q T F T T T F F T T F T F
Given this truth-table, what ordinary English expression can this new truth-functional connective (*) be used to symbolize?
One other broad question:
Suppose there are two sentences a and b. On every interpretation that a is true, b is false. What can you conclude (if anything) about the following argument? Briefly explain.
~(a -> b)
.:. ~b v a
-> :material conditional
v :disjuction/or
Many thanks for help
Plato - apologies, something happened with my spacing.
Yes your table is equivalent to what I tried to put; please see edit.
What would the English phrase be for this? Is there a sentence this could be symbolised with?
Thanks
Actually there are probably many names for this.
As I said, WVO Quine called this the alternative denial operatorr, first discovered by CS Peirce.
I don't remember is Perice had a name for it.
It also goes by the name stroke function,
The chart I posted shows that the other functions can be defined using this operator.
It in effect: "It is false if both statements are true and true otherwise".
Sorry I mistyped this one - still don't understand the answer.
One other broad question:
Suppose there are two sentences a and b. On every interpretation that a is true, b is false. What can you conclude (if anything) about the following argument? Briefly explain.
~(a -> c)
.:. ~b v c
-> :material conditional
v :disjuction/or
This argument is valid in this sense. The formula ~(a -> c) is equivalent to a /\ ~c. Then use the assumption.