∀p∀q∀r((p≡T ∧q≡F ∧r≡T) →[(p∧¬q)⨁r≡T])   TRUE        FALSE   because:     The contrapositive:

For each logical argument, select all the truth assignments for the propositional variables that show the logical argument is invalid. 1) (qV p) P→→q ..p^-q P q TT TF FT F F 2) ¬V¬s r¬s ..r / s r S TT TF FT F F

If p=T, q=unknown and r=F, what is p ∨ r ∧ q?

Write the following in disjunctive normal form using logical equivalences( p ∨q) →(p ∧¬r).

Determine whether the following proposition is a tautology: (¬p∨¬(r⟶q))⟷(p⟶(¬q∧r)) can i get a non handwriting answer so it would be easy to copy please

Suppose that you are given the following logical statement:¬ P ∧ Q → ¬ R ∨ SBased on our discussion of order of operations, which is the correct way to interpretthis?(a) ¬(P ∧ ((Q → (¬R)) ∨ S))(b) (¬(P ∧ (Q → (¬R)))) ∨ S(c) ((¬P) ∧ (Q → (¬R))) ∨ S(d) (¬P) ∧ ((Q → (¬R)) ∨ S)(e) (¬(P ∧ Q)) → (¬(R ∨ S))(f) ((¬P) ∧ Q) → ((¬R) ∨ S)(g) ((¬P) ∧ (Q → (¬R))) ∨ S(h) ((¬P) ∧ (Q → (¬R))) ∨ S(i) (¬P) ∧ ((Q → (¬R)) ∨ S)(j) ¬((P ∧ Q) → (¬(R ∨ S)))

Which of the following are equivalent to:¬((∀x)(∃y)(∀z)(P(x)→(Q(y)∨R(z))))? (Select all that apply.) Group of answer choices (∃x)(¬(∃y)(∀z)(P(x)→(Q(y)∨R(z)))) (∃x)(∀y)(¬(∀z)(P(x)→(Q(y)∨R(z)))) (∃x)(∀y)(∃z)(¬(P(x)→(Q(y)∨R(z)))) (∃x)(∀y)(∃z)(P(x)∧¬(Q(y)∨R(z))))

Determine the validity of the following arguments using truth tables. Which confluence of truth values shows its invalidity? 1. A ⇒BB ⇒A -----------∴A ⇒B 2. (E ∨R ) ∧(E ∨T)R ∧T ------------∴E 3. (O ∨P) ⇒JO ∨¬JP ∨¬JO ⇔¬P -----------∴J ∧¬J

Simplify the proposition using the equivalence laws (C ↔ B) ∧ (((¬B ∨ A) → ¬B) → ¬C)

For each of the following regular expressions over Σ = {a, b}, state 5 strings that are in the language of the regular expression, and 5 strings that are not.  1. (a∗b)∗|a∗2. (Σ∗aaΣ∗)|(Σ∗bbΣ∗)|(ab)∗|(ba)∗|a|b