"All apples are fruits. Some fruits are sour."
Analyzing the Premises
We are given two statements and asked to find a logical conclusion. Let's break down the premises:
- Premise 1: "All apples are fruits." This means the set of all apples is entirely contained within the set of all fruits. If something is an apple, it must also be a fruit. We can represent this as: If $x$ is an apple, then $x$ is a fruit ($Apple \implies Fruit$). In set notation, $A \subseteq F$, where $A$ is the set of apples and $F$ is the set of fruits.
- Premise 2: "Some fruits are sour." This means there exists at least one fruit that is also sour. It does not say that *only* fruits are sour, nor does it say *all* fruits are sour. We can represent this as: There exists an $x$ such that $x$ is a fruit AND $x$ is sour ($ \exists x: (Fruit(x) \land Sour(x)) $). In set notation, the intersection of the set of fruits ($F$) and the set of sour things ($S$) is not empty ($F \cap S \neq \emptyset$).
Testing the Conclusions
Now, let's evaluate each option based on these premises:
Option 1: Some fruits may not be apples.
This statement is logically valid. Premise 1 states that all apples belong to the fruit category ($A \subseteq F$). However, it does not state that the fruit category *only* contains apples. There could be many other types of fruits (like bananas, oranges, etc.) that are not apples. Therefore, it's possible, and logically consistent with the premises, that some fruits are not apples. This conclusion can be drawn.
Option 2: Some apples are not fruits.
This statement is logically invalid. It directly contradicts Premise 1, which explicitly states "All apples are fruits." If all apples are indeed fruits, then it's impossible for some apples *not* to be fruits.
Option 3: All sour things are fruits.
This statement is logically invalid. Premise 2 tells us that *some* fruits are sour ($F \cap S \neq \emptyset$). This implies that the category of sour things overlaps with the category of fruits. However, it doesn't restrict sourness *only* to fruits. There could be other sour things in the world, like lemons (which are fruits), vinegar, or sour candies, that are not fruits. The premise doesn't provide enough information to conclude that *all* sour things must be fruits.
Option 4: All apples are sour.
This statement is logically invalid. Premise 1 relates apples to fruits. Premise 2 relates *some* fruits to being sour. There is no information given that connects *all* apples to the characteristic of being sour. It's possible that some apples are sour, none are sour, or all are sour, but we cannot conclude this logically just from the given statements.
Logical Deduction Summary
Based on the analysis of the premises:
- Premise 1: $A \subseteq F$
- Premise 2: $F \cap S \neq \emptyset$
Only the conclusion "Some fruits may not be apples" is logically supported. The set of fruits ($F$) can contain elements that are not in the set of apples ($A$), which is consistent with $A \subseteq F$ but does not require $A = F$. The other options either contradict the premises or make unsupported claims.
Similar Questions
- All flowers are plants. Some plants are flowering plants. Which conclusion is logically valid?
Two statements are given, followed by three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known f act s, decide which of the conclusions logically follow(s) from the statements.
Statements:
Some carpenters are singers.
All singers are doctors.
Conclusions:
I. No doctor is a carpenter.
II. Some doctors are singers.
III. Some carpenters are doctors.
Three statements are given, followed by three conclusions numbered I, II and III. Assuming the statement s to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
Some machines are coolers.
All coolers are robots.
Some microwaves are coolers.
Conclusions:
I. Some coolers are machines.
II. Some robots are machines.
III. No robot is a microwave.
Three statements are given followed by three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
1. All teachers are students.
2. All principal are teachers.
3. Some principals are doctors.
Conclusions:
I. Some students are teachers.
II. No student is a doctor.
III. Some students are principals.Two statements are given followed by three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
1. All apples are mangoes.
2. Some bananas are mangoes.
Conclusions:
I. Some mangoes are bananas.
II. Some mangoes are apples.
III. No mango is an apple.Three statements are given followed by three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
1. No bed is a chair.
2. All tables are beds.
3. No cupboard is a bed.
Conclusions:
I. No table is a chair.
II. No cupboard is a table.
III. Some beds are tables.
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. No city is a district.
2. Some districts are zones.
3. Some zones are states.
Conclusions:
I. Some zones are districts.
II. Some districts are cities.
lII. No state is a zone.
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 tables are chairs.
2. Some chairs are beds.
3. All beds are goods.
Conclusions:
I. Some chairs are goods.
Il. Some goods are not beds.
Read the given statements and conclusions carefully. Assuming that the information given in the statements is ture, 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 man is engineer.
No engineer is driver.
Some drivers are shop-keepers.
Conclusions:
1. Some men are drivers.
2. No shop-keepers are engineer.
3. Some shop-keepers are not engineers.
Read the given statements and conclusions carefully. Assuming that the information given in the statements is ture, 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 aero-planes are cars.
All helicopters are cars.
All cars are scooters.
Conclusions:
1. All helicopters are scooters.
2. Some aero-planes are helicopters.
3. No aero-plane is helicopter.
Important Questions from 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:
Some students are players.
All players are male.
Conclusions:
I. All males are players.
II. Some males are students.
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 creative is an employer.
All experts are creative.
All workers are experts.
Conclusions:
I. No employer is an expert.
II. No worker is an employer.
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:
Some actors are choreographers.
All choreographers are producers.
Not a single producer is a director.
Conclusions:
I. Some actors are directors.
II. Not a single actor is a director.
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. All flowers are tulips.
2. No tulips are whites.
Conclusions :
I. All tulips are flowers.
II. Some tulips are whites.
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 rats are dogs.
Some rats are hens.
Conclusions:
I. Some rats are dogs.
II. Some hens are rats.
