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.
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:
All dancers are talented.
Some girls are dancers.
Conclusions:
I. Some girls are talented.
II. All talented are girls.
III. All girls are talented.
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 directors are actors.
No actor is a producer.
All choreographers are directors.
Conclusions:
I. No choreographer is producer.
II. Some actors are choreographers.
III. No director is a producer.
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 follows from the statements.
Statements:
All lemons are plums.
All plums are dates.
Some dates are mangoes.
Conclusions:
I. Some lemons are mangoes.
II. Some mangoes are plums.
III. All lemons are dates.
IV. Some mangoes are dates.
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 cards are postcards.
Some cards are envelopes.
All envelopes are copies.
Conclusions:
I. Some copies are envelopes.
II. Some postcards are copies.
III. Some cards are copies.
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 employees are tax-payers.
Some employees are farmers.
Some farmers are doctors.
Conclusions:
I. No farmer is a tax-payer.
II. Some farmers are tax-payers.
