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 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.
Consider the given statement(s) to be true and decide which of the given conclusions/assumptions can definitely be drawn from the given statement.
Statement 1: All elephants are men.
Statement 2: All men are socks.
Conclusion I: Some socks are elephants.
Conclusion II: All elephants are socks.In the question, a word is represented by only one set of numbers as given in any one of the alternatives. The sets of numbers given in the question are represented by two classes of alphabets in two matrices given below. The columns and rows of Matrix 1 are numbered from 0 to 4 and that of Matrix II are numbered from 5 to 9. A letter from these matrices can be represented first by its row and next by its column, e.g., 'A' can be represented by 04, 12, etc., and 'U' can be represented by 59, 66, etc. Similarly, you have to identify the set for the word 'ROOT'.
MATRIX I
0 1 2 3 4 0 B C D E A 1 D E A B C 2 C D E A B 3 A B C D E 4 E A B C D MATRIX II
5 6 7 8 9 5 R O N T U 6 T U R O N 7 O N T U R 8 U R O N T 9 N T U R O Consider the given statement/s to be true and decide which of the given conclusions/assumptions can definitely be drawn from the given statement.
Statements: 1. All fish are tortoise.
2. No tortoise is a crocodile.
Conclusion: 1. No crocodile is a fish.
II. No fish is a crocodile.
Consider the given statements to be true and decide which of the given conclusions/assumptions can definitely be drawn from the given statement.
Statements: 1. All books are novels.
2. Some novels are poems.
Conclusions: I. Some books are poems.
II. Some poems are novels.Consider the statement to be true and decide which of the conclusions logically follow:
Statement:
All dogs are animals.
All animals are living beings.
Conclusion
I:Dog is not an animal.
II. Dog is an animal.In the question, a word is represented by only one set of numbers as given in any one of the alternatives. The sets of numbers given in the matrices are represented by two classes of alphabets as in two matrices given below. The columns and rows of Matrix I are numbered from 0 to 4 and that of Matrix II are numbered from 5 to 9. A letter from these matrices can be represented first by its row and next by its column, e.g., 'A' can be represented by 01, 13, etc., and 'S' can be represented by 55, 66, etc. Similarly, you have to identify the set for the word 'BOTH'.
MATRIX I
0 1 2 3 4 0 F A N O I 1 I O F A N 2 A N O I F 3 O F I N A 4 N I A F O MATRIX II
5 6 7 8 9 5 S E H B T 6 H S E T B 7 B T S E H 8 E H T B S 9 T S E H B Consider the given statement/s to be true and decide which of the given conclusions/assumptions can definitely be drawn from the given statement.
Statement I: All astronomers are scientists.
Statement II: Some scientists are shopkeepers.
Conclusion I: All astronomers are shopkeepers.
Conclusion II: All astronomers are scientists.
Conclusion III: Some shopkeepers are astronomers.
Conclusion IV: All scientists are astronomers.A word is represented by only one set of numbers as given in any one of the options. The sets of numbers are formed using two matrices below. The rows and columns of Matrix I are numbered 0 to 4 and Matrix II are numbered 5 to 9. A letter is represented by its row and column numbers. For example, ‘G’ can be coded as 12 or 21, and ‘L’ as 76 or 67.
Find the correct code for the word ‘LIFE’.
Consider the given statement/s to be true and decide which of the given conclusions/assumptions can definitely be drawn from the given statement:
Statements: Some cars are caves.
Conclusion: I. Some cars are not buses
II. Some caves are buses
III. No cave is a bus
IV. Some caves are cars
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.
