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If p and q are statement variables. T is a tautology and c a contradiction. Applying...
Construct a truth table for the following statement. Determine if the statement is a tautology, contradiction, or neither. (-pуp)V(-рлр) Fill in the blanks in the truth table (-pу p)V(-рл р) p V p p / T Does the truth table show a tautology, contradiction, or neither? Contradiction Tautology Neither
Construct a truth table for the given statement. Identify if it is a tautology, contradiction, or neither. Fill in the truth table. -q Is the statement a tautology, contradiction, or neither? Contradiction O Tautology O Neither
Verify the logical equivalences using the theorem below: (p ∧ ( ~ ( ~ p ∨ q ) ) ) ∨ (p ∧ q) ≡ p Theorem 2.1.1 Let p, q, and r be statement variables, t a tautology, and c a contradiction. The following logical equivalences are true. 1. Commutativity: p1q=q1p; p V q = 9VP 2. Associativity: ( pq) Ar=p1qAr); (pVq) Vr=pv (Vr) 3. Distributivity: PA(Vr) = (p19) (par); p V (qar) = (pVg) (Vr) 4. Identity: pAt=p:...
(d) Determine if the compound proposition is a tautology, contradiction or a contingency ( -1 (p + q) + np. Clearly justify your answer.
Discrete Math I'm confused with the questions listed below. Can you please solve and explain in detail? how it transforms one to the other to get the answer? Using propositional logic properties and other logical equivalences (not truth tables), prove the following statements: 1. (p Vq) V (p V -q) is a tautology 2. ((p-+ r) Л (q r) Л (pv q)) _+ r is a tautology 3. (pVq) Л (-р Л q) is a contradiction 4. (1-p) Λ (p...
Express each English statement using logical operations V, Lambda, - 1. and the propositional variables t, n, and m defined below. The use of the word "or" means inclusive or. t: The patient took the medication. n: The patient had nausea. m: The patient had migraines. There is no way that the patient took the medication. a) -n b) -(-m) c) -m d) -t Define the following propositions: s: a person is a senior. y: a person is at least...
Please generate a truth table and answer "Is the compound statement a tautology?" (p ↔ q) ↔ [ (q → p) ∨ (p → ~ q) ]
help with all of them please thanks in advance 1. Determine whether the given statement is a tautology, a contradiction or neither. Justify your answer. (p Aq) → (pVq)) 2. Determine the intersection and the union of the intervals (3,5), [4, 7] and [5, 8). 3. For each positive number t, let At be the interval (-2, t]. Determine the union Ut>O At and the intersection n t>o At of the family {At t>0}. 4. prove that the set {5kke...
In this assignment you will write code that will prove both equations for three logical equivalences (pick any three except the double negative law). Below is the list of logical equivalences. Please create a program that allows a user to test logical equivalences and have proof of their equivalency for the user. The rubric is below. Submit screen shots of the code, input, and output of the program. Theorem 2.1.1 Logical Equivalences Given any statement variables p, q, and r,...
QUESTION 13 The TF-statement (q^~p) →~(~ qvp) is a(n) A contradiction B.tautology C. contingency D. equivalence E. antecedent