Use the laws of propositional logic to prove that the following
compound propositions are logically equivalent.A. ? ↔ (? ∧ ?) and ? → ?B. ¬(? ∨ (? ∧ (? → ?))) and ¬? ∧ (? → ?)
Is the argument valid? Use rules of inference and laws of logic
to prove or disprove (no Truth tables)
1. If John has talent and works very hard, then he will get a
job. If he gets a job, then he’ll be happy. Hence if John is not
happy, then he either not worked very hard or does not have
talent.
2.For spring break Marie will travel to Cancun or Miami. If she
goes to Cancun, she will not visit...
Complete the following statements.Two compound propositions p and q in propositional logic are
logically equivalent if . . ..An argument form in propositional logic is valid if . . ..A theorem is a statement that . . ..A statement that is assumed to be true is called a(n) . . ..A proof is a valid argument that . . ..
Propositional Logic
Using operator properties and other logical equivalences (not
truth tables), prove these statements.
1. ((p→r)∧(q→r)∧(p∨q))→r (tautology)
2. ¬(q→p)∧(p∧q∧s→r)∧p (contradiction)
3. (p→q)∧(p→r)≡p→(q∧r)
2. Determine whether the following Propositional Logic
statements are valid or invalid arguments. You may use a truth
table, proofs using rules of inference, or resolution (specify
which method you are using).
(a) p→q, ~q→r, r; ∴p
(b) ~p∨q, p→(r∧s), s→q; ∴q∨r
(c) p→(q→r), q; ∴p→r
Represent the following argument in the symbolic notation of
Propositional Logic: If this argument is sound, it’s valid, but
it’s not sound, so it’s invalid. (Remember how to use slashes in
propositional logic)
Propositional Logic
Is the following formula in Conjunctive Normal Form? Why? Why
not?
(¬A) n (A u B) n ¬(A u B)
where A and B are propositional variables.