Consider the Following Domain, Assignment of Objects in the Domain $\lor$

question 43

Multiple Choice

consider the following domain, assignment of objects in the domain, and assignments sets to predicates.
Domain = {1, 2, 3, ..., 28, 29, 30}
a = 1
e = 21
b = 2
f = 23
c = 4
g = 27
d = 20
h = 29
Ex = {2, 4, 6, ..., 28, 30}
Ox = {1, 3, 5, ..., 27, 29}
Px = (2, 3, 5, 7, 11, 13, 17, 19, 23, 29}
Sxyz = The set of all triples such that the first is the sum of the second and third
{<2, 1, 1>, <3, 1, 2>, <3, 2, 1>, <4, 1, 3>, <4, 2, 2>, <4, 3, 1>, <5, 1, 4>, ... }
-Given the customary truth tables, which of the following theories is modeled by the above interpretation?

• A) (∃x)(∃y)[(Ex • Ey) • Sfxy] (∃x)(∃y)[(Ox • Oy) • Sfxy]
• (∀x){Ex ⊃ {(∃y)(∃z)[(Ey • Ez) • Sxyz)] \( \lor \) (∃y)(∃z)[(Ox • Oy) • Sxyz]}}
• B) (∃x)(∃y)[(Ex • Ey) • Sdxy]
• (∃x)(∃y)[(Ox • Oy) • Sdxy]
• (∀x){Ex ⊃ {(∃y)(∃z)[(Ey • Ez) • Sxyz)] \( \lor \) (∃y)(∃z)[(Ox • Oy) • Sxyz]}}
• C) (∃x)(∃y)[(Ex • Ey) • Sdxy]
• (∃x)(∃y)[(Ox • Oy) • Sdxy]
• (∀x){Ex ⊃ {(∃y)(∃z)[(Ey • Ez) • Sxyz)] • (∃y)(∃z)[(Ox • Oy) • Sxyz]}}
• D) (∃x)(∃y)[(Ex • Ey) • Sfxy]
• (∃x)(∃y)[(Ox • Oy) • Sfxy]
• (∀x){Ex ⊃ {(∃y)(∃z)[(Ey • Ez) • Sxyz)] • (∃y)(∃z)[(Ox • Oy) • Sxyz]}}
• E) (∃x)(∃y)[(Ex • Ey) • Sdxy]
• (∃x)(∃y)[(Ox • Oy) • Sdxy]
• (∀x){Ox ⊃ {(∃y)(∃z)[(Ey • Ez) • Sxyz)] \( \lor \) (∃y)(∃z)[(Ox • Oy) • Sxyz]}}

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Definitions:

Quantitative

Refers to the measurement of something in terms of quantity or amount.

Categorical

Pertaining to data that can be divided into specific groups or categories that are mutually exclusive.

Data

Collected information or facts, typically numerical, that are used as a basis for reasoning, discussion, or calculation.

Categorical Variable

A type of variable that can take on one of a limited, and usually fixed, number of possible values, assigning each individual or other unit of observation to a particular group or nominal category.