Question

In: Statistics and Probability

The following defines what logical property: A pair of propositions (wffs) P,Q that have the same...

The following defines what logical property: A pair of propositions (wffs) P,Q that have the same truth value under every interpretation.

consistency? proposition? argument? equivalence ?

Solutions

Expert Solution


Related Solutions

FOR EAICH PAIR OF PROPOSITIONS P AND Q STATE WHETHER ON NOT p=q p=(s→(p ∧¬r)) ∧...
FOR EAICH PAIR OF PROPOSITIONS P AND Q STATE WHETHER ON NOT p=q p=(s→(p ∧¬r)) ∧ ((p→(r ∨ q)) ∧ s), Q=p ∨ t
Let p and q be propositions. (i) Show (p →q) ≡ (p ∧ ¬q) →F (ii.)...
Let p and q be propositions. (i) Show (p →q) ≡ (p ∧ ¬q) →F (ii.) Why does this equivalency allow us to use the proof by contradiction technique?
prove or disprove using logical equivalences (a) p ∧ (q → r) ⇐⇒ (p → q)...
prove or disprove using logical equivalences (a) p ∧ (q → r) ⇐⇒ (p → q) → r (b) x ∧ (¬y ↔ z) ⇐⇒ ((x → y) ∨ ¬z) → (x ∧ ¬(y → z)) (c) (x ∨ y ∨ ¬z) ∧ (¬x ∨ y ∨ z) ⇐⇒ ¬y → (x ↔ z)
Using logical equivalence laws, show that (((p v ~ q) ⊕ p) v ~p) ⊕ (p...
Using logical equivalence laws, show that (((p v ~ q) ⊕ p) v ~p) ⊕ (p v ~q) is equivalent to p v q. v = or, ~ = not, ⊕ = exclusive or (XOR). Please show the steps with the name of the law beside each step, thanks so much!
Explain the logical structure of the following set of propositions - a theory. 1.The set of...
Explain the logical structure of the following set of propositions - a theory. 1.The set of languages accepted (decided) by deterministic Turing machines = the set of languages accepted (decided) by nondeterministic Turing machines 2. PATH belongs to P 3. TAUTOLOGY is a member of coNP 4. 2 definitions for NP (1 in terms of a polynomial verifier 2 in terms of a nTM) are equivalent 5. PSPACE = NPSPACE 6. NP is a subset of PSPACE 7. SAT belongs...
Two compound propositions p and q in propositional logic are logically equivalent if . . ..
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 . . ..
Let p and q be the propositions p:You drive over 65 miles per hour. q: You...
Let p and q be the propositions p:You drive over 65 miles per hour. q: You get a speeding ticket. Write these propositions using p and q and logical connectives. a) You do not drive over 65 miles per hour. b) You drive over 65 miles per hour, but you do not geta 1 speeding ticket. c) You will get a speeding ticket if you drive over 65 miles per hour. d) If you do not drive over 65 miles...
The ‘Exclusive OR’ operation (also called XOR) between two propositions p and q is defined as...
The ‘Exclusive OR’ operation (also called XOR) between two propositions p and q is defined as follows: p ⊕ q = (p ∨ q) ∧ ¬(p ∧ q) Using laws of propositional logic prove the following: (i.) Exclusive OR is commutative, i.e., p ⊕ q ≡ q ⊕ p. (ii.) p ⊕ p is a contradiction. (iii.) Conjunction distributes over Exclusive OR, i.e, for any proposition r, r ∧ (p ⊕ q) ≡ (r ∧ p) ⊕ (r ∧ q)....
The ‘Exclusive OR’ operation (also called XOR) between two propositions p and q is defined as...
The ‘Exclusive OR’ operation (also called XOR) between two propositions p and q is defined as follows: p ⊕ q = (p ∨ q) ∧ ¬(p ∧ q) Using laws of propositional logic prove that conjunction distributes over Exclusive OR, i.e, for any proposition r, r ∧ (p ⊕ q) ≡ (r ∧ p) ⊕ (r ∧ q). Clearly state which law you are using in each step.
Convert the logical statement ~(P || ~R) || (Q -> R) to conjunctive normal form. Please...
Convert the logical statement ~(P || ~R) || (Q -> R) to conjunctive normal form. Please explain the steps!!
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT