I was looking at an exercise where it asked the following:
So, for the third column, I just put which was correct but I didn't understand what meant. I have seen but I haven't the arrow. Are they the same thing?
Thanks a bunch!
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1Yes. – fuglede Jan 7 '14 at 16:57
The symbol is a connective. It's a symbol which connects two propositions in the context of propositional logic (and its extensions, first-order logic, and so on).
The truth table of is defined to be that is false if and only if is true and is false.
Indeed this is the same meaning of , but the difference is that is a statement about propositions, whereas is a proposition. In some contexts, though, people don't make this distinction between material implication (the connective) and logical implication (the arrow). But they are not the same thing in every context of propositional logic.
answered Jan 7 '14 at 16:58
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I'll add here that A. N. Prior's textbook Formal Logic has parts of it which read like the following: "Rule: Detachment (, DD ) and (In all cases the sole rule beside substitution is E-detachment: , E . And in my opinion Prior's symbolism comes as clearer here than writing {E, } , since the "" symbol suggests that one transitions from the left-hand side to the right hand side. – Doug Spoonwood Nov 10 '14 at 19:26
Given , then we have .
or implies .
The two arrows mean the same thing.
answered Jan 7 '14 at 16:57
It is a material conditional, or otherwise known as implies , or if , then
The truth table for that is as follows
p q p implies q
T T T
T F F
F T T
F F T
can also be written as .
In computer science, can be rewritten as (not p) or q, or !p||q
Now, although I am only a rising 8th grader taking geometry, I can assure you that there is no difference to the arrows. I have seen a two sided arrow (p<-->q), but that is different. The single arrow just indicates a conditional statement.
