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![Construct proof for the following argument within the system of sentential logic:
1. -Q 2 -R
Premise
2. -(P & Q)
Premise
3. -(-P &-R) Premise /:. -(P = R)
7:18 AM
Prove within the system of sentential logic that "anything follows from a contradiction", i.e., prove the following argument:
1. P& -P
Premise /:. Z
7:18 AM
Construct proof for the following argument within the system of sentential logic:
1. (A & B) > (C V D)
2. -(C V (B > X))
3. -[D =-(X & Y)]
Premise
Premise
Premise
4. -Aɔ -Z
Premise /:. -Z
7:18 AM
Construct proof for the following argument within the system of sentential logic:
1. -(-Dɔ -C) ɔ -B
Premise
2. -Bɔ A
Premise
3. (YV C) & (~C V-A)
Premise /:. DV (A V Y)
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Construct proof for the following argument within the system of sentential logic:
1. (A & B) ⊃ (C V D) Premise
2. ~(C V (B ⊃ X)) Premise
3. ~[D ≡ ~(X & Y)] Premise
4. ~A ⊃ ~Z Premise /: . ~Z
Construct proof for the following argument within the system of sentential logic:
1. ~(~D ⊃ ~C) ⊃ ~B Premise
2. ~B ⊃ A Premise
3. (Y V C) & (~C V ~A) Premise /: . D V (A V Y)
Prove the following proposition to be a tautology by constructing a proof for the following theorem within the system of sentential logic:
~(P ≡ Q) ⊃ (P ≡ ~Q)
Construct proof for the following argument within the system of sentential logic:
1. ~Q ⊃ ~R Premise
2. ~(P & Q) Premise
3. ~(~P & ~R) Premise /:. ~(P ≡ R)
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Construct proof for the following argument within the system of sentential logic:
1. (A & B) ⊃ (C V D) Premise
2. ~(C V (B ⊃ X)) Premise
3. ~[D ≡ ~(X & Y)] Premise
4. ~A ⊃ ~Z Premise /: . ~Z
Construct proof for the following argument within the system of sentential logic:
1. ~(~D ⊃ ~C) ⊃ ~B Premise
2. ~B ⊃ A Premise
3. (Y V C) & (~C V ~A) Premise /: . D V (A V Y)
Prove the following proposition to be a tautology by constructing a proof for the following theorem within the system of sentential logic:
~(P ≡ Q) ⊃ (P ≡ ~Q)
Construct proof for the following argument within the system of sentential logic:
1. ~Q ⊃ ~R Premise
2. ~(P & Q) Premise
3. ~(~P & ~R) Premise /:. ~(P ≡ R)
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- 1. Prove or refute: (∀x, y, z, w)(B(x, y, z) ∧B(w, y, z) →B(x, w, y)).2. Prove or refute: (∀x, y, z, w)(B(x, y, z) ∧B(x, w, y) →B(w, y, z)).arrow_forwardPlease Help with the question below: Suppose you are given some facts in First-Order Logics: a) Andi is a professor b) All professors are people. c) Ani is the dean. d) All Deans are professors. e) All professors consider the dean a friend or don’t know him. f) Everyone is a friend of someone. g) People only criticize people that are not their friends. h) Andi criticized Ani. Prove that: Ani is not Andi’s friend.arrow_forwardProve ⊢ (¬A → A) → A in Hilbert deductive system. Note: In addition to the axioms and rule of inference of H, you may use any of the derived rules and/or theorems 3.20-3.30 (as numbered in the textbook). You may not use theorem 3.31, as this is precisely that theorem.book Mordechai Ben-Ari Mathematical Logic for Computer Science Third Edition Prove {¬A} ⊢ (¬B → A) → B in Hilbert deductive system. Note: In addition to the axioms and rule of inference of H, you may use any of the derived rules and/or theorems 3.20-3.30 (as numbered in the textbook). book Mordechai Ben-Ari Mathematical Logic for Computer Science Third Edition PLEASE solve these with the help of 3 axioms and 1 rule of inference with the derived proof 3.20-3.30.arrow_forward
- Construct proof for the following argument within the system of sentential logic: 1. (A & B) ⊃ (C V D) Premise2. ~(C V (B ⊃ X)) Premise3. ~[D ≡ ~(X & Y)] Premise4. ~A ⊃ ~Z Premise /: . ~Zarrow_forwardIs the following sentence a proposition? If it is a proposition, determine whether it is true or false. “In the year 2000, Montreal was the capital of Quebec.”arrow_forwardAlert dont submit AI generated answer.arrow_forward
- i need answer of all. if any answer will be skipped, your answer will be rejected. only complete answer will be accepted. b) Make a truth table for the statement ¬P ∧ (Q → P). What can youconclude about P and Q if you know the statement is true? a) Make a truth table for the statement (P ∨ Q) → (P ∧ Q). c) Make a truth table for the statement ¬P → (Q ∧ R).arrow_forwardSuppose that Q(x) is "x+1 = 2x", where x is a real number. How many of the following statements are TRUE? • Q(2) is true • there exists x such that Q(x) is true • for every x, Q(x) is true O O 0 1 02 0 3arrow_forwardThe Sentence : " the negation of "if p then q" is logically equivalent to "p and not q .............................This can be restated symbolically as followsarrow_forward
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