if c v r and ~r are both premises? then c must be... true  false  cbd LOGIC

Q: Consider the two following statements: 1. A Sufficient condition to buy the pink flower is I will…

A: False

Q: Show that the following are logically equivalent using logic algebra a) pv (p^q) = p b) (p^q) v (~pv…

A: To Show- Show that the following are logically equivalent using logic algebra. p ∨ p ∧ q ≡ p p ∧ q…

Q: Consider the following premises: • PV q Then the valid conclusion is

A: Given, 1. p∨q2. p→m   Using Modus ponens on (2) 3. m

Q: Consider the following premises : Every sane person can do logic. No cat can do logic. Those who are…

A: c)Logical persons cannot serve in the government is not a valid conclusion. d)Those who serve in the…

Q: Show that -p → (q → r) and q → (p V r) are logically equivalent

A: We have to show that ¬p→(q→r) and q→(p∨r) are logically equivalent. To show logically equivalent…

Q: Consider the following propositions: p="lt is cloudy" q="lt is rainy" r="I will play outside" s="|…

A:

Q: y implication, P implies Q, the contrapositive of the implication is logically equivalent to P…

A: Introduction: a proposition or theorem formed by contradicting and swapping the subject and…

Q: 1) Yes/No Is the following logical expression a proposition: ∀z ∃y Q(x, y, z)?

A:

Q: The statement: not (p or not q) is logically equivalent to O (not p) or q O (not p) and (not q) O…

A: Concept:

Q: (6) Assume that all of the premises given bvelow are true. Using all of them, what can o logically…

A:

Q: (b) Consider the statement: if x 0, then x < y. State the hypothesis P(x, y) and the conclusion…

A:

Q: which of the following propositions is logically equivalent to A v (A ∧B) v (A ∧ B ∧ C) Select one:…

A: Given:- A v (A ∧B) v (A ∧ B ∧ C)To find :  Which is logically equivalent to above…

Q: (b) Consider the statement: if x 0, then r< y. State the hypothesis P(x,y) and the conclusion Q(x,…

A: Consider the statement " If x≤y+∈, ∀∈&gt;0, then x≤y."

Q: Prove the following statements (Premises) using the natural deduction laws: Premises Conclusion D>…

A: Given to prove:  D→A∧BB→L∧M              D     M Proof: I. If D, then A∧B that is both A and B. II.…

Q: Express the following propositions in symbols, where p,q and r are defined as follows: p: Neil is a…

A: Hi! You ha We are given the following. p: Neil is a big eater. q: Len has a big voice. r: Jeric…

Q: Prove that the following statement is valid by using resolution to prove that its negation is…

A:

Q: Derive the conclusion of the following argument using the method of conditional proof where…

A: Given:- 1.A⊃(B*D) 2.-B∨E                                     /A⊃E 3.A⊃

Q: On your work determine if p → (q → r) is logically equivalent to either of the following statements…

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Q: Which of the following statements are logically equivalent? (a) P → (Q ^ R). (b) (P → Q) ^R (c)(P=…

A:

Q: Show that the following are logically equivalent using logic algebra (p^q) v (~pv (p^~q)) = T

A: We need to prove the logical equivalence of: p∧q∨~p∨p∧~q≡T using logic algebra.

Q: Write a logical proof to prove that the following argument is valid. p (qAr) pV s 1 V SL . r

A:

Q: Match the following sentences expressed in first-order logic to their English counterparts: 1.∀ x ∀…

A: Given statements are

Q: Show via Venn diagrams that the logical implication (A = B) is equivalent to the following…

A:

Q: Which statement exchanges the hypothesis and conclusion of a conditional? O inverse O converse O…

A: Converse StatementsConverse and inverse are connected concepts in making conditional statements. To…

Q: ¬p→(q→r) = q→(pvr) are logically equivalent?

A: 7p→(q→r)=q→(pvr)

Q: 5. For the given premises, determine a suitable conclusion so that the argument is valid. (a) p q, I…

A: Given

Q: Prove that the statements ∀x∀yP(x,y) and ∀x∀yP(y,x) are logically equivalent .

A: Given statement is ∀x∀yP(x,y)  and   ∀x∀yP(y,x)   are logically equivalent . We have to prove that…

Q: Show that by using Laws that if the compound statement is logically equal. [p ⋀ (~ (~p⋁q))] ⋁…

A:

Q: Determine whether the following is a valid translation from the English sentence to predicate logic.…

A: In this question, concept of predicate logic is applied. Predicate Logic The study of Predicate…

Q: The following arguments are valid. Give a formal deduction for each. a. Premises: A → (BC), (C →…

A: What is Natural Deduction: Natural deduction is a type of proof calculus used in logic and proof…

Q: 7. Show that the following a) pV (p A q) = p b) (p A q) v (~p v (p ^ ~q)) = T are logically…

A: I have done solution step by step by mentioning all law of algebra....go through the solution

Q: 2. Given that P = p ^ (q vr) and Q = p V (q¬r). By using bi-conditional statement, show that whether…

A: By using bi-conditional statement, two statements P and Q are equivalent only if the bi-conditional…

Q: 1) Show that the following pairs are logically equiw a) р^(qVr) (pAq)V(pAr) b) pV(qAr) (pVq)A(pVr)

A: Given: p∧q∨r; p∧q∨p∧rp∨q∧r; p∨q∧p∨r

Q: Use propositional logic, rules of inference to prove that the following arguments are valid: (A →…

A:

Q: Are these statements logically equivalent? Are they satisfiable? Give your reason. ¬p → (q → r) and…

A:

Q: Express the following propositions in symbols, where p, q and r are defined as follows: p: Neil is a…

A: 'While Len has a big voice, Neil is not a big eater'. Here both the things are simultaneously true,…

Q: b) Show that (p A q) → r and (p → r) ^ (q → r) are not logically equivalent.

A:

Q: Use propositional logic, rules of inference to prove that the following arguments are valid: (A →…

A:

Q: Use propositional logic to prove that the following arguments are valid: (a) (A- -C) A (-C→-B) a B-A…

A:

Q: X implies (Y and Z) is logically equivalent to (X implies Y) or (X implies Z) A) True B) False

A: Given statement is  X implies (Y and Z) is logically equivalent to (X implies Y) or (X implies Z)

Q: Prove, using logical arguments, that (AU B)° = A°NB°. %3D

A: Use the necessary properties.

Q: prove these deductions (a) x∩y=∅, (z⊂x), ∴(z∩y)=∅ (b) p⊂q, ∴(r∖q) = (r∖p)∖q

A:

Q: State the rule of inference by which its conclusion follows from its premise or premises. (CVD) ɔ…

A:

Q: Construct direct proofs to show that the following symbolic arguments are valid. Commas mark the…

A: Since you have asked multiple questions, we will solve the first three questions for you. If you…

Q: Determine the valid conclusion, given the following premises: 1. -p v q vr 2. -4 3. -r Therefore, O…

A:

Q: Which of the following statement(s) is(are) TRUE?

A: Test is that whether the mean amount of pay farmers received in a month is less than 8000 pesos.

Q: (6) Assume that all of the premises given below are true. Using all of them, what can you logically…

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Q: Assume that p and q are true statements and that r is a false statement. Which " of the following…

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Q: 7. Use all of the premises to determine a valid conclusion for the following argument. ~m Vt t - ~d…

A: