Answer:
(a)
( ∃x ∈ Q) ( x > √2)
There exists a rational number x such that x > √2.
( ∀x ∈ Q) ( ( x ≤ √2)
For each rational number x, x ≤ √2.
(b)
(∀x ∈ Q)(x² - 2 ≠ 0).
For all rational numbers x, x² - 2 ≠ 0
( ∃x ∈ Q ) ( x² - 2 = 0 )
There exists a rational number x such that x² - 2 = 0
(c)
(∀x ∈ Z)(x is even or x is odd).
For each integer x, x is even or x is odd.
( ∃x ∈ Z ) (x is odd and x is even)
There exists an integer x such that x is odd and x is even.
(d)
( ∃x ∈ Q) ( √2 < x < √3 )
There exists a rational number x such that √2 < x < √3
(∀x ∈ Q) ( x ≤ √2 or x ≥ √3 )
For all rational numbers x, x ≤ √2 or x ≥ √3.
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