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: All javascript are binary. All binary are minecraft. All roblox are minecraft. Conclusions: I. Some javascript are roblox. II. Some javascript are minecraft. III. All javascript are minecraft.
Only conclusions II and III follow
Analyzing Statements and Conclusions in Logical Reasoning
This problem requires us to analyze logical statements and determine which conclusions logically follow. We are given three statements relating four entities: javascript, binary, minecraft, and roblox. We must assume these statements are true, even if they contradict common knowledge.
Statements Analysis
Let's break down the given statements:
- Statement 1: All javascript are binary. This means that every item belonging to the category 'javascript' is also included in the category 'binary'.
- Statement 2: All binary are minecraft. This means that every item belonging to the category 'binary' is also included in the category 'minecraft'.
- Statement 3: All roblox are minecraft. This means that every item belonging to the category 'roblox' is also included in the category 'minecraft'.
From Statement 1 and Statement 2, we can form a direct link using the concept of transitivity:
If All javascript are binary (J → B) and All binary are minecraft (B → M), then it logically follows that All javascript are minecraft (J → M).
Statement 3 tells us that Roblox is a subset of Minecraft, just like Javascript (via Binary) is a subset of Minecraft. However, there is no direct relationship established between Javascript and Roblox based purely on these statements.
Conclusion Analysis
Now, let's evaluate each conclusion based on our analysis of the statements:
- Conclusion I: Some javascript are roblox.
We know All javascript are minecraft (from Statements 1 & 2) and All roblox are minecraft (from Statement 3). Both Javascript and Roblox are categories within Minecraft. However, the statements do not provide any information about whether the Javascript category overlaps with the Roblox category within Minecraft. They could overlap, or they could be entirely separate. Therefore, this conclusion does not necessarily follow.
- Conclusion II: Some javascript are minecraft.
From Statements 1 and 2, we deduced that All javascript are minecraft. If it is true that 'All' members of one group are members of another, it is logically true that 'Some' members of the first group are members of the second. For example, if all apples are fruits, then it's also true that some apples are fruits. Thus, this conclusion logically follows from the statements.
- Conclusion III: All javascript are minecraft.
As directly derived from combining Statement 1 (All javascript are binary) and Statement 2 (All binary are minecraft) through the rule of transitivity, this conclusion is logically true. If every javascript item is binary, and every binary item is minecraft, then every javascript item must be minecraft.
Summarizing Conclusions that Logically Follow
Based on the analysis:
- Conclusion I (Some javascript are roblox) does not follow.
- Conclusion II (Some javascript are minecraft) follows.
- Conclusion III (All javascript are minecraft) follows.
Therefore, only conclusions II and III logically follow from the given statements.
| Statements | Relationship |
|---|---|
| All javascript are binary. | Javascript ⊆ Binary |
| All binary are minecraft. | Binary ⊆ Minecraft |
| All roblox are minecraft. | Roblox ⊆ Minecraft |
| Conclusion | Logically Follows? | Reasoning |
|---|---|---|
| I. Some javascript are roblox. | No | No direct link between Javascript and Roblox is given. Both are subsets of Minecraft but may not overlap. |
| II. Some javascript are minecraft. | Yes | If All javascript are minecraft (from Statements 1 & 2), then Some javascript are minecraft must also be true. |
| III. All javascript are minecraft. | Yes | Directly follows from Statements 1 and 2 (Transitivity: J → B → M). |
Revision Table: Key Concepts in Syllogism
| Concept | Explanation | Example |
|---|---|---|
| All A are B | Every member of set A is a member of set B. | All cats are animals. |
| Some A are B | At least one member of set A is a member of set B (could be all). | Some students are tall. |
| No A are B | No member of set A is a member of set B. | No dogs are birds. |
| Transitivity | If A is related to B, and B is related to C, then A is related to C in a specific way (e.g., All A are B, All B are C → All A are C). | All dogs are mammals. All mammals are animals. → All dogs are animals. |
Additional Information: Understanding Syllogistic Reasoning
Syllogistic reasoning is a type of logical argument where a conclusion is drawn from two or more premises (statements). These arguments are a fundamental part of deductive logic, where if the premises are true, the conclusion must also be true.
In competitive exams, questions on statements and conclusions test your ability to understand the relationships given in the statements and derive only those conclusions that are strictly implied by these relationships, without using any outside knowledge. It's crucial to stick only to the information provided in the statements.
Representing statements using Venn diagrams can often help visualize the relationships between the categories and verify whether a conclusion is valid. For instance, "All A are B" means the circle for A is entirely inside the circle for B. "Some A are B" means the circles for A and B overlap. "No A are B" means the circles for A and B do not overlap.
In this specific problem:
- All javascript are binary: Javascript circle inside Binary circle.
- All binary are minecraft: Binary circle inside Minecraft circle.
- All roblox are minecraft: Roblox circle inside Minecraft circle.
This setup shows Javascript is inside Binary, which is inside Minecraft. Roblox is also inside Minecraft, but its position relative to Javascript is not fixed by the statements; it could overlap, be separate, or even contain Javascript (though the "All J are B" and "All B are M" structure makes the latter less likely based on standard interpretations, sticking to minimal assumptions is key). This visual confirms that "All javascript are minecraft" and thus "Some javascript are minecraft" are true, while "Some javascript are roblox" is not necessarily true.
Similar Questions
- Read the following statement carefully and identify the conclusion that follows.
Statement:
All poets are writers. Some writers are critics. No critic is a fool.
Conclusions:
I. Some poets are critics.
II. Some writers are not fools. - Statements: All dancers are artists. No artist is lazy.
Conclusions: I. No dancer is lazy. II. Some lazy are dancers. - Read the following statement carefully and identify the conclusion that follows.
Statement:
All oranges are fruits. No fruit is a vegetable. All vegetables are green.
Conclusions:
I. No orange is green.
II. No orange is a vegetable. - Read the following statement carefully and identify the conclusion that follows.
Statement:
All kids are students. Some students are athletes. No athlete is a scholar.
Conclusions:
I. Some kids may be athletes.
II. No kid is a scholar. - Statements: Some keys are locks. Some locks are doors.
Conclusions: I. Some keys are doors. II. All locks being keys is a possibility. - Read the following statement carefully and identify the conclusion that follows.
Statement:
All musicians are artists. Some artists are dancers. No dancer is blind.
Conclusions:
I. Some artists are not blind.
II. All blind are not dancers. Statements: Some pens are papers. All papers are books. Conclusions: I. Some pens are books. II. All books are pens.
Read the following statement carefully and identify the conclusion that follows.
Statement:
All birds are animals. Some animals are tigers. No tiger is a bird.
Conclusions:
I. Some tigers are birds.
II. Some animals are not birds.
- Statements: All dogs are cats. Some cats are rats. Conclusions: I. Some rats are dogs. II. All dogs are rats.
Read the following statement carefully and identify the conclusion that follows.
Statement:
All pens are blue things. Some blue things are plastic. No plastic is recyclable.
Conclusions:
I. Some pens are plastic.
II. Some blue things are not recyclable.
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.
