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

Q: 1.7 Applying Rules From the premises "p and not q" and "r and not s", we can derive the conclusion…

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Q: For each numbered line that is not a premise in each of the formal proofs that follow state the rule…

A: We prove the given argument by using rules of inference or replacement rules.

Q: Given the following hypotheses, construct an argument and draw a conclusion (if possible) using…

A: (a)The given hypothesis are,It is snowing today.If you played soccer, then it wasn’t snowing.If you…

Q: In p-->q what's the premise ?

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Q: W./.:// If P: p v(qar) and Q :(pvq)^(pvr) are J a logically Equivalent ( Prove that P Q)?

A: Two statement forms are called logically equivalent if, and only if, they have identical truth…

Q: 7. Establish the validity of the following arguments: (p v q) A (a +r)A (p → s) ASTA (p v q).

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

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

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Q: Show that the arguments form with the following premises • (p A t) → (r V s) • q → (u ^ t) • u → p…

A: Given premises are p∧t→r∨s q→u∧t u→p ¬s q

Q: Are the following two logical statements equivlent ~( p v q) ~ p ^ ~q

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Q: The following statements are true except (p v q) (¯p v¬q) (p → q) (¯p v q) O (p v q) (q v p) pa (q v…

A: Let us draw the truth tables for each of the following  1) ~p∨q⇔~p∨~q p q p∨q ~p∨q ~p ~q ~p∨~q…

Q: Is the following argument valid? Provide a proof for your answer. p =⇒ (q ∧ r)  ∼q − − − − − − − − −…

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

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Q: 1. Determine the rule of inference used in the following arguments. А. а — (b лс) (ьле) —>d .'.a d…

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Q: Create a proof for the following argument. 1. Av (D v C) 2. -C 3. (A v D) ɔ (B v C) I Bv C

A: We prove the given argument by using rules of inference.

Q: Show that each of the following conclusions (C) follows from the given premise (b) P1: (p V q) → (r…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Complete the table below to prove the proposition by applying the rules of inference. Reasons 1. J…

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Q: Show that the following are logically equivalent 1. 2. ¬ {[(pvq)^r] v¬q} v (¬r^q) ↔ q [(p^-q) vr]…

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Q: If P is true, Q is false, and R is true, what is the truth value of (PAR)= (Q V R)?

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Q: p V q p → ~q p → r .'. r Is the above argument valid?

A: To determine whether the below argument is valid or not. p∨qp→~qp→r¯∴r

Q: Consider the premises. P:- All athletes practice. Q- If one practices, then s/he becomes strong. R:=…

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

A: 7p→(q→r)=q→(pvr)

Q: Use the rules of inference to show that if the following premises are given • Vr(P(x) ^ R(x)) •…

A: GivenP(x)→(Q(x)∧S(x))P(a)→(Q(a)∧S(a)) for any  a  in the domain  ...Universal  on…

Q: Verify that the following statements are tautologies. 1) Transitive Law [(p → q)A(q → r)] → (p → r)…

A: 1)Transitive law[(p→q)∧(q→r)]→(p→r)2)Law of Excluded Middle p∨~p3)Law of Syllogism[p∧(p→q)]→q

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 the 8 inference rules to prove the following arguments. a) ~P (Q v P) - R P v S…

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Q: 1. ~(AV B) — с 2. ~A 3. ~С Show that (1) – (3) entails B

A: We have to show that (1)-(3) entails B using the rule of inference.

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

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Q: QUESTION 1 Using rules of inferences, show that the following argument is valid: SL V JL

A: Given: p→q ¬r∧¬s ¬q→r ∴¬p∧s

Q: Show that the propositions: pue JAbal(nd) v (b^ d)]L ( are equivalent.

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Q: The following is correct application of Hypothetical Syllogism: [RƆ (QƆ S)] D (C V D) (C V D) Ɔ (Q )…

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Q: Indicate whether the following arguments are deductive or inductive.

A: Deductive and Inductive:-   On the off chance that the arguer accepts that the reality of the…

Q: Given the premises: P P→9 SVI 9-1 Arrive at the conclusion using rules of inference: svt

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Q: If p is false, q is true, and r is true, find the truth value of the statement. (~pv-q) v ~r

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Q: State the rule of inference by which its conclusion follows from its premise or premises. (Q כ (P…

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Q: The law of syllogism states that if p→q and q→r, then p→r. O True O False

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Q: Given: AM BM Prove: AD = BC

A: We have to prove AD¯≅BC¯.

Q: Is the following argument valid? Assume that premises 1 and 2 are true. 1. If it is raining, then…

A: Conditional Reasoning: 1. If it is raining, then Tim will stay in the house. 2. It is raining.

Q: Is ∼((∼p ∧ q) ∨ (∼p ∧ ∼q)) ∨ (p ∧ q)  logically equivalent to p?

A: Verify whether ~~p∧q∨~p∧~q∨p∨q is logically equivalent to p using truth table as shown below.

Q: Are the statements P → ¬Q AR and ¬P v (¬Q ^ R) logically equivalent? Explain why.

A: Let p and q be two propositions.  If the propositions p and q are logically equivalent, then they…

Q: Below is the proof for the following argument using rules of inference: .-(r V q) 1 pA-g Hypothesis…

A: Given 2 = p→¬r 3 = p

Q: 1. Use the first four rules of inference to derive the conclusions of the following symbolized…

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Q: I Prove the validity of the following argument: 1. p→9 → 9 (¬r) V (¬q)

A: Q1 asked and answered.

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

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Q: are the following two logical statements equialent  ( p v q) v r  p v ( q v r )

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Q: Determine if the following arguement is valid or not ( ΡA)-R -PV ¬Q -R

A: We prove the deduction to be invalid key assigning suitable truthful values. Let,

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

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

A: We have used here the rule     P v Q    ~Q  Therefore  Q

Q: 7.) V W TV = XW VA = WA ΤΑΧΑ Given: Prove: ATVA = AXWA Statements Reasons

A: We will prove this by checking the postulates of triangle triangles as shown below we know that If…

Logic and Proofs

Discrete mathematics deals with the separated values of data such as integers. It is widely used in the practical field of computer science and mathematics. By knowing discrete mathematics one can improve their reasoning and problem-solving capabilities. Discrete mathematics became popular after the boom of computers which operate in discrete steps and store data in discrete bits. It also useful in studying computer programming, algorithms, and cryptography.