Use an ordinary proof (not conditional or indirect proof): 1. A ⊃ (Q ∨ R) 2. (R • Q) ⊃ B 3. A • ∼B / R ≡ ∼Q
Use an ordinary proof (not conditional or indirect proof): 1. A ⊃ (Q ∨ R) 2....
Use an ordinary proof (not conditional or indirect proof):1. ∼N⊃ (∼R⊃ C) 2. R⊃ N 3.∼C / N
use 18 rules of inference to solve the following problem. Do not use conditional proof, indirect proof, or assumed premises.for each proof you must write the premises in that proof. 1. X v Y prove /S v Y 2. z 3.( x•z)---> s
Please give proof direct or indirect with numbered justification/law. (a) t→r, ¬(r∨¬q), ¬t→p, p→(s∨¬q) ⇒ s (b) (s→q)∧(p→t) ⇒ (s∨p)→(q∨t)
Match the following: item 1. Indirect proof which assumes the opposite of a statement and shows this creates a logical inconsistency item 2, Indirect proof applied to a statement of the form P→Q which instead proves-Q→-P. item 3. Proves a "there exists" statement by finding a specific element for which the statement is true item 4. Disproves a "for all" statement by finding a specific element for which the statement is false. item 5. Proof where a statement is split...
Philosophy: Use the 8 rules of implication and the 10 rules of replacement PLUS conditional proof to prove the arguments 1. (A ∨ B) ⊃ (C • E) 2. ( D ⊃ E) ⊃ F / A ⊃ F
Philosophy: Use the 8 rules of implication and the 10 rules of replacement PLUS conditional proof to prove the arguments 1. (A ∨ B) ⊃ (C • E) 2. ( D ⊃ E) ⊃ F / A ⊃ F
Philosophy: Use the 8 rules of implication and the 10 rules of replacement PLUS conditional proof to prove the arguments 1. A ⊃ D 2. (A • D) ⊃ F / A ⊃ F
25. (2 points) Below is a proof presented as a proof by contradiction. Restate the proof, using the same ideas, as a proof of the contrapositive of the proposition. Proposition: The sum of a rational number and an irrational number is irrational. Proof: Suppose BWOC that there existr e Q and neR-Q such that run e Q. Sincer is rational, r = for some p, q E Z. Sincer+ne Q, also r+n= for some a, b e Z. Now: r...
Indirect Proofs: Prove Problems 5 - 7 using either proof by contradiction or proof by contraposition. AT LEAST ONE MUST USE PROOF BY CONTRADICTION! 7) For integers c, if c = ab and the ged(a,b) = 1, then a and b are perfect squares. (Hint: If a and b are not perfect squares, what type of number are they?)
3. Prove valid by a deductive proof: 1. S (TR) 2. R R 3. (V S)-(W T)/ .. V D~W 4. Prove valid by a deductive proof: 1. (B. L)VT 2. (BVC) (~LO M) 3.~M /.. T 5. Prove valid by a deductive proof: 1. E.(FVG) 2. (E.G)(HVI) 3. (~HV I)(E . F) /.. H= I