For each pair of statements, choose the one that is true. Oze {y, z} O {z} E {y, z} (a) o {6, 7, 8} c {1,2, 3, 4, ...} o {6, 7, 8} e {1,2, 3, 4, ...} (b) o {3} c {2, 3} (c) O 3 c {2, 3} Or s {r, s, t} (d) Orz {s, t, u}

Q: Give direct and indirect proofs of: p→q,¬r→¬q,¬r⇒¬p. p→¬q, ¬r→q, p⇒r. a∨b, c∧d, a→¬c⇒b.

A: Direct proof :  step  reason 1. p→q premise  2.¬p→¬q premise  3. ¬r premise  4. ¬q 2,3,MP…

Q: Istribution 1 P(Y y) 0 009 0 376 0 167 0 061 0 016 y 3. 4. Which one of the following statements is…

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Q: For each pair of statements, choose the one that is true. O6 c {5, 6, 7} (a) O 6 {5, 7, 8} o {9, 11,…

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Q: Which one of the following statements is true?

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Q: Let R={y,p}, S={z,p,u}, and T={r,y,p,u,z}, For each of the following questions, enter T if the…

A: Given that R={y,p} ,S={z,p,u} ,and T={r,y,p,u,z}1) R has the element y, but S does not have y in it.…

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Q: For each pair of statements, choose the one that is true. Ofe (e,f) (a) ohe le.f) o (6, 7, 8) E {1,…

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

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Q: One of the following statements is true:

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Q: Given: p: It is the month of January; q: It is cold; r: it is windy; s: it is humid. Statements: If…

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Q: Which of the following statements is always true?

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Q: Determine if the following formula is a tautology, contradiction, or neither. (p∧q)⊕(¬p∨¬q)

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Q: For each pair of statements, choose the one that is true. Og c {q, r} (a) o {a) c {q, r} o {g) g…

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Q: Determine which, if any, of the three statements are equivalent. (a) (a) If the pay is good and…

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Q: Let A = {2,4, 6, 8}, B = {3,4,5,6} and D = {4,5}, Which of the following statements is/are true?…

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Q: Consider the first-order logic formula 3x P(a, x) → vy P(b, y) and the interpretation domain D = {1,…

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Q: 7. For each of the following, determine if the statement is (i) a self-contradiction, (ii) a…

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Q: Given: If X, then not Y. If not Y, then Z. Y is true. So:

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Q: 6. Simplify these propositions. a) (p → q ) → (p A q) b) ¬ (p^ q ) v ( ¬p ^ q) c) ((p V (r V q))…

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Q: Which one of the following statements is True?

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Q: Let P(x,y,z) denote the statement "x + y < z, " where x, y, z e Z*. What is the truth value of each…

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Q: Is (p ^ q) → (p V r) a tautology? Prove or disprove it.

A: We will check whether the given statement is true or false.

Q: 9. Which of the following statements are true ? (i) If A = (x : x² = 4, x e N), B = {- 2}, then A +…

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Q: Which of the following models are counter-models that shows that is not a logical consequence?…

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Q: Find the all statements by the truth tables: 1 (pr) v (q→r) = (p^q) → r 2 (p→q) ^ (pr) = p → (q^r) 3…

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

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Q: Which of the following pairs of statements are different from each other? A. (p⇒q)/p ⇒ q B. (p⇒ q)/p…

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Q: 20. Which of the following statements is true?

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Q: Let x e {1, 2} and y e {1, 4}, consider a predicate P(x, y) defined as P(x, y): 4 divides (x² + 3y).…

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Q: Which among the following statements is (are) false? * O vxVy,M(x,y)=Vyvx,M(x,y) O…

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Q: Which of the following statements are true? (2x-14)9>0: xE(7, 0) (2x2 – 18)(x -8) 0: xE(-1,3)u (4,…

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Q: 3. Let the statements A, B be A: (not p) and q, B: (not p) or (not q). If p 0 and q = 1, then !! %3D…

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