Consider the following statement: ∀x ∈ Z, [(2x + 4 > 0) ∨ (4 - x2 ≤ 0)] Which one of the following alternatives provides the correct simplification of the negation of the given statement such that the not-symbol (¬) does not occur to the left of any quantifier?

Database System Concepts
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Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
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Chapter1: Introduction
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Consider the following statement:

∀x ∈ Z, [(2x + 4 > 0) ∨ (4 - x2 ≤ 0)]

Which one of the following alternatives provides the correct simplification of the negation of the given statement such that the not-symbol (¬) does not occur to the left of any quantifier?

Select one:
a.
O b.
O
[Vx € Z, [(2x + 4> 0) v (4- x² < 0)]]
= 3x € Z₁¬[(2x + 4 > 0) v (4 - x² ≤ 0)]
= 3x € Z, [-(2x + 4 > 0) ^ ¬(4 - x² ≤ 0)]
= 3x € Z, [(2x + 4 < 0) ^ (4 - x² ≥ 0)]
O d.
[VX €Z, [(2x + 4 > 0) v (4 - x² ≤ 0)]]
= VX € Z, [(2x + 4 > 0) v (4 - x² ≤ 0)]
= Vx € Z, [¬(2x + 4 > 0) ^ ¬(4 - x² ≤ 0)]
[(0 < zx - t) v (0 s t + xz)] ‘Z > XA =
C. [VX = Z, [(2x + 4> 0) v (4- x² ≤ 0)]]
= 3x € Z, [(2x + 4> 0) v (4-x² ≤ 0)]
[(0 s zX - Đ)LV (0 < t + XZ)L] ‘Z > XE =
= 3x € Z, [(2x + 4 ≤ 0) ^ (4 - x² > 0)]
[VX = Z, [(2x + 4 > 0) v (4 - x² ≤ 0)]]
S
= 3x = Z, [(2x + 4 > 0) ^ (4 - x² ≤ 0)]
= 3x = Z, [1(2x + 4> 0) v ¬(4 - x² ≤ 0)]
= 3x € Z, [(2x + 4 ≤ 0) v (4 - x² > 0)]
Transcribed Image Text:Select one: a. O b. O [Vx € Z, [(2x + 4> 0) v (4- x² < 0)]] = 3x € Z₁¬[(2x + 4 > 0) v (4 - x² ≤ 0)] = 3x € Z, [-(2x + 4 > 0) ^ ¬(4 - x² ≤ 0)] = 3x € Z, [(2x + 4 < 0) ^ (4 - x² ≥ 0)] O d. [VX €Z, [(2x + 4 > 0) v (4 - x² ≤ 0)]] = VX € Z, [(2x + 4 > 0) v (4 - x² ≤ 0)] = Vx € Z, [¬(2x + 4 > 0) ^ ¬(4 - x² ≤ 0)] [(0 < zx - t) v (0 s t + xz)] ‘Z > XA = C. [VX = Z, [(2x + 4> 0) v (4- x² ≤ 0)]] = 3x € Z, [(2x + 4> 0) v (4-x² ≤ 0)] [(0 s zX - Đ)LV (0 < t + XZ)L] ‘Z > XE = = 3x € Z, [(2x + 4 ≤ 0) ^ (4 - x² > 0)] [VX = Z, [(2x + 4 > 0) v (4 - x² ≤ 0)]] S = 3x = Z, [(2x + 4 > 0) ^ (4 - x² ≤ 0)] = 3x = Z, [1(2x + 4> 0) v ¬(4 - x² ≤ 0)] = 3x € Z, [(2x + 4 ≤ 0) v (4 - x² > 0)]
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