Select the Best Translation into Predicate Logic, Using the Following

question 176

Multiple Choice

select the best translation into predicate logic, using the following translation key:
b: Britain
c: Charles
e: Elizabeth
t: Tescos
Px: x is a person
Qx: x is a Queen of England
Wx: x is a woman
Exy: x is more exalted than y
Ixy: x is in y
Pxy: x shops at y
Sxy: x is a son of y
-Charles and his two sons are not the most exalted people in Britain.

• A) (∀x){{Ixb • Px • (∀y)[(Iyb • x≠y) ⊃ Exy]} ⊃ [x≠c • (∀y)(Syc ⊃ x≠y)]}
• B) (∀x){[Ixb • Px • (∃y)(Exy • Iyb)] ⊃ [x≠c • (∀y)(Syc ⊃ x≠y)]}
• C) Icb • (∃x)[Px • Ixb • Exc • (∃y)(∃z)(Syc • Szc • Iyb • Izb • y≠z • Exy • Exz)]
• D) Icb • (∃x)[Px • Ixb • (∀y)(Exy) • x≠c • (∃y)(∃z)(Syc • Szc • Iyb • Izb • y≠z • x≠y • x≠z)]
• E) ~(∀x)[(Ixb • Px) ⊃ Ecx] • ~(∀x)(∀y){Sxc • Syc • (∀z)[(Pz • Izb) ⊃ (Ezx • Eyz)]}

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Definitions:

Smallest Observation

The smallest observation, also known as the minimum value, is the lowest value in a set of data points.

3rd Quartile

A value below which 75% of the data points in a dataset fall.

Negatively Skewed Distribution

A probability distribution that is characterized by a long tail on the left side, indicating that the bulk of the values are concentrated to the right.

Smallest Observation

The lowest value recorded in a data set.