#88. Determine whether these pairs of statements arelogically equivalent. Justify your answer.a) Vx(P(x)Q(x)) and VxP(x)VxQ(x)b) 3x(P(x) V Q(x)) and 3xP(x) v 3xQ(x).->You may copy the sign , A, V, →, +, =, 3!, 3,1.

Equivalence using quantifiers. ∀(P(x)) →Q(x)) and ∀xP(x) →∀xQ(x) This is not actually logically…

Answered: B. Determine whether these pairs of…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Draw the truth table of (A→ B) ˄ (B → A) and (A Ú B) ˄ (¬B Ú A). Determine from the truth table whether (A→ B) ˄ (B → A) is logically equivalent to ((¬A Ú B) ˄ (¬B Ú A)
a) Show that (a V b → c) → (a Ab → c) is a tautology but its converse is contingency. b) If p → q is false, what is the truth value of ((¬p) ^ q) → (p V q)? Explain your answer. c) Let L(x) be the statement "x visited London", let P(x) be the statement "x visited Paris" and let N(x) be the statement "x visited New York". Express the statement "None of your friends visited London, Paris and New York." in terms of C(x), D(x), F(x), quantifiers, and logical connectives where the domain consists of all your friends. a) Let A, B, U and V be any sets such that A C U and B C V. Is (A × B) C (U X V)? Justify your answer. b) Suppose f: R → Z where f(x) =[2x – 11. i. If A = {x |1 < x < 4}, find f (A). ii. If B = {3,4,5,6,7}, find f (B). iii. If C = {-9, –8}, find f-1(C). c) Let f:R → R be defined by f (x) = 2x2 + 2x – 12. Is fone-to-one? Justify your answer. a) Find the number of positive integers not exceeding 120 that are divisible by 3 or 4. 0 1 0 01 0 0 0 0 0 0. Find A[9]. 0 1 0 0 0 Lo o o 1…
Construct a truth table to determine whether the following expression is logically equivalent or not. [(a n -c) -→ -b]> a → (b -→ c)
State whether the propositions in parts (a) through (j) are TRUE or FALSE considering the following sets: X = (a, 1, (a, a), [a, 1], 0) Y = (a, 3, (a), [1, a]} (a) a EX (b) (a) EX (c) [a, 1] EX (d) [a, 1] € Y (e) Ø EX (f) Ø EY (g) Ø≤X (h) {0} ≤X (i) ([a, 3]) EXXY () (a, 1) x Y= (1, a) x Y
1. Prove formally that the following statements are equivalent: For any two formulas A and B, (a) A = B; (b) A → B is valid; (c) A^¬B is unsatisfiable.
i) Carefully explain why p ↔ q can be written as “p is necessary and sufficient for q”. ii) Verify the second part of De Morgan’s laws, ∼ (p∨q) ≡ (∼ p) ∧(∼ q), in two ways: (a) Explain it using conversational English, using your own particular examples of statements for p and q. (b) Use a truth table.
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)
Could you assist me with this problem? I'm having difficulty understanding it and would really appreciate your guidance. Would you mind providing a thorough, step-by-step explanation to help me comprehend it more effectively?
Use a truth table to demonstrate that these two statements are logically equivalent:((p ∧ ¬q) ∨ (p ∧ q)) ∧ q and (p ∧ q).
Show that the argument is valid, indicating the rule of inference or logical equivalence applicable to each step. ∃x ( C(x) ∧ ( ¬ S(x) → ( V(x) ∨ W(x) ) ) )∀x ( V(x) → ¬ C(x) )¬ ∃x ( W(x) ∧ C(x) ) _________________________∴ ∃x ( S(x) ∧ ¬ W(x) )
b) For each of the compound proposition, state either TRUE or FALSE if p and r are TRUE and q is FALSE. i. (p→q)→(¬p→r) ii. (p+q)^(¬q+r)
Question # 2 : Show that each of these conditional statements is a tautologyby using truth tables. a) (p∧q)→p b) p→(p ∨q) c) ￢p →(p →q) d) (p∧q)→(p →q)

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B. Determine whether these pairs of statements are logically equivalent. Justify your answer. a) Vx(P(x)→ Q(x)) and VxP(x)→ VxQ(x) b) 3x(P(x) V Q(x)) and ExP(x) V IxQ(x).