The statements below are followed by two conclusions labeled I and II. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts. decide which conclusion(s) logically and definitely follow(s) from the information given in the statements. Statements: Some cows are deer. Some deer are fishes. Conclusion: I. Some cows are fishes. II. Some fishes are cows.
Statement Analysis
We are given two premises:
- 1. Some cows are deer.
- 2. Some deer are fishes.
The task is to determine if the given conclusions logically follow from these premises, assuming the premises are true.
Conclusion Assessment
The two conclusions provided are:
- I. Some cows are fishes.
- II. Some fishes are cows.
Note that Conclusion II is the converse of Conclusion I and therefore logically equivalent in this context.
Logical Deduction
Let C represent the set of cows, D represent the set of deer, and F represent the set of fishes.
- Premise 1 states that there is at least one member common to sets C and D. Mathematically, this is $C \cap D \neq \emptyset$.
- Premise 2 states that there is at least one member common to sets D and F. Mathematically, this is $D \cap F \neq \emptyset$.
The question is whether these two conditions guarantee that $C \cap F \neq \emptyset$.
The premises only establish connections between C and D, and D and F. They do not provide a direct link between C and F. It is possible that the subset of deer that are cows is entirely separate from the subset of deer that are fishes.
Consider a scenario:
- Cows = {Cow A, Cow B}
- Deer = {Deer X, Deer Y, Cow A}
- Fishes = {Fish P, Fish Q, Deer Y}
In this case:
- Cow A is a deer, satisfying Premise 1 ($C \cap D = \{Cow A\}$).
- Deer Y is a fish, satisfying Premise 2 ($D \cap F = \{Deer Y\}$).
- However, no cow is a fish ($C \cap F = \emptyset$).
Result
Since we can construct a valid scenario where the premises are true but the conclusions are false, neither Conclusion I nor Conclusion II logically and definitely follows from the given statements.
Important Questions from Conventional Syllogism
Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements:
1. Some flowers are chemicals.
2. Some chemicals are herbs.
Conclusions:
I. No flower is a herb.
II. Some flowers are herbs.
Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements:
All students are teachers.
All teachers are professors.
Conclusions:
1. All students are professors.
2. All professors are students.
3. No teacher is a professor.
Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements:
I. Some dentists are surgeons.
II. All the surgeons are doctors.
Conclusions:
I. Some dentists are doctors.
II. No surgeons are dentists.
The statements below are followed by two conclusions labelled I and II. Assuming that the information in the statements is true, even if it appears at variance with generally established facts. decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.
Statements:
1) Some angers are griefs.
2) Some griefs are loves.
Conclusion:
I. Some griefs are angers.
II. Some loves are griefsThe statements below are followed by three conclusions labeled I, II and III. Assuming that the Information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.
Statements:
All balls are boats.
All boats are cars.
Conclusions:
I. Some cars are balls.
II. All balls are cars.
III. All cars are balls.
