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18 Ity SO for I VEN is a ( mathematical ) predicate with the domain N JUSTIFY 3 19 . For predicate formulas A ( x ) .
9. The formula ∃x((C(x) ∩ F(x)) ⇒ Y (x)) represents sentence: Some blue flowers are yellow in a domain X 6= ∅
JUSTIFY: y n
10. For any predicates A(x), B(x), the formula ((∀xA(x) ∪ ∀xB(x)) ⇒ ∀x(A(x) ∪ B(x))) is a predicate tautology
JUSTIFY: y n
11. ∃xA(x) ⇒ ∀xA(x) is a predicate tautology.
JUSTIFY: y n
12. For predicate formulas A(x), B(x), ¬∀x(A(x) ∩ B(x)) ≡ (¬∀xA(x) ∪ ∃x¬B(x))
JUSTIFY: y n
13. ∀x(A(x) ⇒ A(x)) is a predicate tautology
JUSTIFY: y n
14. For predicate formulas A(x), B(x), ∃x(A(x) ∪ B(x)) ≡ (∃xA(x) ∪ ∃xB(x))
JUSTIFY: y n
15. ∀x ∈ R(x 2 < 0) ⇒ ∃x ∈ R(x 2 < 0) is a true mathematical statement
JUSTIFY: y n
16. ∀x2<0(x + 1 = 4) ⇒ ∃x2<0(x + 1 = 4) is a true mathematical statement in the set R of real numbers
JUSTIFY: y n
17. ¬∀n∃x(x < 1+n n+1 ) ≡ ∃n∀x(x ≥ 1+n n−1 ))
JUSTIFY: y n
and also the following in the picture
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