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: No almond is a fruit. Some cashews are almonds. Conclusions: I. No fruit is an almond. II. All fruits are cashews.
Only conclusion I follows
Understanding Logical Reasoning with Statements and Conclusions
This question asks us to analyze given statements and determine which conclusions logically follow from them. We must assume the statements are true, even if they contradict common knowledge, and only use the information provided in the statements to evaluate the conclusions.
Analyzing the Given Statements
Let's break down the two statements provided:
- Statement 1: No almond is a fruit.
- Statement 2: Some cashews are almonds.
Statement 1 tells us that the set of "almonds" and the set of "fruits" have absolutely no members in common. They are disjoint sets.
Statement 2 tells us there is an overlap between the set of "cashews" and the set of "almonds". There are some items that are both cashews and almonds.
Visualizing the Statements (Conceptual)
We can think of this using conceptual circles or sets:
- The circle for "Almonds" and the circle for "Fruits" do not touch at all.
- The circle for "Cashews" and the circle for "Almonds" overlap in some area.
From this, we know that the overlapping area between Cashews and Almonds cannot contain any Fruits because no Almonds are Fruits.
Analyzing the Given Conclusions
Now let's look at the conclusions and see if they are supported by the statements:
- Conclusion I: No fruit is an almond.
- Conclusion II: All fruits are cashews.
Evaluating Conclusion I: No fruit is an almond
Statement 1 says "No almond is a fruit." This establishes a relationship of complete separation between almonds and fruits. If it is true that no member of the 'almond' group belongs to the 'fruit' group, then it must also be true that no member of the 'fruit' group belongs to the 'almond' group. This is a direct logical consequence of the first statement. The relationship "No A is B" is equivalent to "No B is A".
Therefore, Conclusion I logically follows from Statement 1.
Evaluating Conclusion II: All fruits are cashews
Statement 1 tells us about the relationship between almonds and fruits. Statement 2 tells us about the relationship between cashews and almonds. We know some cashews are almonds, and no almonds are fruits. This doesn't provide any information about the relationship between fruits and cashews. Fruits could be entirely separate from cashews, they could overlap with cashews, or cashews could be entirely contained within fruits. The statements do not give us enough information to conclude that all fruits are cashews.
Therefore, Conclusion II does not logically follow from the given statements.
Summary of Conclusion Analysis
- Conclusion I: No fruit is an almond — This is a valid inference from "No almond is a fruit".
- Conclusion II: All fruits are cashews — This cannot be determined from the given information.
Determining Which Conclusion(s) Follow
Based on our analysis, only Conclusion I logically follows from the given statements.
Revision Table: Statements and Conclusions
| Statements | Conclusions | Logically Follows? | Explanation |
|---|---|---|---|
| No almond is a fruit. | I. No fruit is an almond. | Yes | This is the contrapositive/converse equivalence of the statement "No A is B" meaning "No B is A". |
| Some cashews are almonds. | II. All fruits are cashews. | No | The statements provide no information to establish a universal relationship between fruits and cashews. |
Additional Information: Types of Logical Statements
In logic problems like this, statements typically fall into categories based on quantity (All, Some, No) and quality (affirmative, negative):
- Universal Affirmative (All A are B): Every member of set A is also a member of set B.
- Universal Negative (No A is B): No member of set A is a member of set B (Sets A and B are disjoint).
- Particular Affirmative (Some A are B): At least one member of set A is also a member of set B (Sets A and B overlap).
- Particular Negative (Some A are not B): At least one member of set A is not a member of set B.
Understanding these basic structures helps in analyzing the relationships described in the 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.
