i was wondering if anybody could explain/solve the folowing so i can
What does it mean for a logical statement to be valid, and what does it
mean for it to be satisfiable?
Which of the following statements are valid, satisfiable, or neither?
(a) fire => smoke
(:lol: Smoke => fire
(c) (fire => smoke) => (\~smoke => \~fire)
note:\~ refers to NOT, i could not draw the proper sign
any comment would be really appreciated
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Not sure if this is a homework assignment, but so you know, this isn’t
the place (and there shouldn’t be any place) to have other people do
your homework for you.
Secondly, you must tell us what the => symbol means in this context.
I checked Wikipedia, and the pages are written from a retrospective and
abstract perspective, rather than explaining things without assuming
prior knowledge and experience, so I can’t make sense of it.
I’m guessing that valid means that a statement is consistent or correct.
For example, 4+5 is valid, 4+/5 is not.
I’ll also guess that satisfiable means that the logical statement has at
least one solution. For example, 2*3 = ? has a solution of 6.
Infinity*zero = ? doesn’t necessarily have a solution.
Seriously, have you ever heard of Google?
But, to get you started, “valid” means “satisfied under all possible
instances” and “satisfied” applies to any one instance. IOW, valid means
true for all instances, but you’d say a case satisfies the logic
statement. (Keep in mind, “instances” are constrained to the domain the
logic statement is about.)
“x is purple”
- If we substitute “eggplant” for x, then the statement is satisfied.
- I we substitute “Amy”, well, it’s not satisfied. Amy is not purple.
This is all basic stuff you’d find in any math book on predicate