"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
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.
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 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 books are grapes.
Some grapes are fruits.
Conclusions:
I. No grape is a book.
II. Some grapes are books.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 fans are radio.
All fans are light.
Conclusion I: Some radios are light.
Conclusion II: Some lights are radio.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 scissors are spoons.
All spoons are plates.
Conclusions:
1. Some plates are spoons.
2. Some spoons are scissors.
3. Some plates are scissors.
Read the given statements and conclusions carefully. Assuming that the information given in the statement 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 boat is ship.
Some ships are rods.
Conclusions:
I. No boat is rod.
II. Some rods are ships.
III. Some rods are not boats.
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 bottles are glasses.
All glasses are jugs.
Conclusions:
I. All bottles are jugs.
II. All jugs are bottles.
III. Some glasses are bottles.
In the following question below are given some statements followed by some conclusions. Taking the given statements to be true even if they seem to be at variance from commonly known facts, read all the conclusions and then decide which of the given conclusion logically follows the given statements.
Statements:
I. Some pen are black.
II. Some pen are blue.
III. No black is red.
Conclusions:
I. No pen is red.
II. Some blue are black.
III. Some black are pens.In the following question below are given some statements followed by some conclusions. Taking the given statements to be true even if they seem to be at variance from commonly known facts, read all the conclusions and then decide which of the given conclusion logically follows the given statements.
Statements:
I. All cups are plates.
II. All plates are red.
Conclusions:
I. All cups are red.
II. All plates are cups.
III. All red are plates.In the following question below are given some statements followed by some conclusions. Taking the given statements to be true even if they seem to be at variance from commonly known facts, read all the conclusions and then decide which of the given conclusion logically follows the given statements.
Statements:
I. Some sky are blue.
II. Some blue are soft.
Conclusions:
I. Some sky are soft.
II. Some soft are sky.What will come in the place of the question mark (?) in the following equation if '+' and '-' are interchanged and 'x' and '÷' are interchanged?
108 × 2 − 14 ÷ 6 + 27 = ?
Important Questions from Syllogism
The statements below are followed by 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 twenty are thirty.
All thirty are forty.
All forty are sixty.
All sixty are seventy.
Conclusions:
I. Some forty are thirty.
II. Some seventy are sixty.
III. No thirty is twenty.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 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 Strong are animals.
Some animals are Tigers.
All Tigers are Sharp.
Conclusions:
I. Some Strong are Sharp.
II. No Strong is Sharp.The statements below are followed by conclusions labelled 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:
Some women are weak.
Some weaks are female.
All female are iron.
All iron are gold.Conclusions:
I. Some weaks are iron.
II. Some gold are weaks.
III. Some women are female.
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 teaspoons are glasses.
All teddies are teaspoons.
Conclusions:
I. Some teddies are glasses.
II. Some glasses are teddies.
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:
All bangles are rings.
Some rings are toys.
Some toys are dolls.
Conclusions:
I. Some rings are bangles.
II. Some dolls are rings.
