Hey I have a mathematical reasoning question that I need help with, The four sen
ID: 3010276 • Letter: H
Question
Hey I have a mathematical reasoning question that I need help with,
The four sentences this question refers to are:
All pidgeons are quibblers.
Some pidgeons are quibblers.
No pidgeons are quibblers.
Some pidgeons are not quibblers.
Suppose we have a first-order language with the usual variables, connectives, quanti- fiers, equality, and two one-place relations, P and Q. P(r) is supposed to mean "r is a pidgeon" and Q(z) is supposed to mean "r is a quibbler 2. If there are no pidgeons, but there are some quibblers, in the universe the four sen tences in question 1 are talking about, which of them must be true? If, instead, there are no quibblers, but there are some pidgeons in that universe, which of the four sentences must be true? (Do, please, explain why in each case.)Explanation / Answer
If there are no pidgeons but there are some quibblers.
a) All pidgeons are quibblers. May or may not be true because there can be some quibblers which are not pidgeons in the universe.
b) Some pidgeons are quibblers. May or may not be true because there can be some quibblers which are not pidgeons in the universe.
c) No pidgeons are quibblers. It must be true as because only quibblers are in the universe.
d) Some pidgeons are not quibblers.May or may not be true because there can be some quibblers which are not pidgeons in the universe.
If there are no quibblers but there are some pidgeons in universe .
a) All pidgeons are quibblers. False
b) Some pidgeons are quibblers. May or may not be true because there can be some pidgeons which are not in the universe.
c) No pidgeons are quibblers. It must be true as because only pidgeon are in the universe.
d) Some pidgeons are not quibblers.May or may not be true because there can be some pidgeons which are not quibblers in the universe.