Which of the assumptions given in the options is implicit in the statements? Statements: All Explosives are Sound. Some Bombs are Exclusively Sound. Some light are Bombs but not Sound.
Some Sounds are only Bombs.
Understanding Statements and Implicit Assumptions
This question asks us to identify which of the given options is an implicit assumption within the provided statements. An implicit assumption is something that is not directly stated but is taken for granted or implied by the statements.
Analyzing the Given Statements
Let's break down each statement carefully:
- Statement 1: All Explosives are Sound.
This is a universal affirmative statement. It means the category 'Explosives' is completely contained within the category 'Sound'. If something is an Explosive, it must also be Sound.
- Statement 2: Some Bombs are Exclusively Sound.
This is a particular affirmative statement with an exclusivity clause. The phrase "Exclusively Sound" when applied to "Some Bombs" implies that there is a group of Bombs that are Sound, and critically, these specific Bombs belong only to the Sound category among the categories discussed in these statements (Explosives, Bombs, Sound, Light). This means these particular Bombs are Sound, and they are not Explosives, and they are not Light.
- Statement 3: Some light are Bombs but not Sound.
This is a particular statement indicating an overlap between 'Light' and 'Bombs', but specifying that this overlapping group is outside the 'Sound' category. So, there is a group that is both Light and Bomb, and this group is definitely not Sound.
Evaluating the Options
Now, let's examine each option to see if it must be true based on the statements, or if the statements rely on it being true (i.e., it's an implicit assumption).
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Some Sounds are only Bombs.
This option states that there exists a group of entities that are Sound, belong to the 'Bombs' category, and belong only to the 'Bombs' category among the relevant categories (meaning they are not Explosives and not Light).
Let's look at Statement 2 again: "Some Bombs are Exclusively Sound." As we interpreted, this means there is a group of Bombs that are Sound, and these Bombs are not Explosives and not Light. This group of entities is therefore:
- In the category 'Bombs'.
- In the category 'Sound'.
- Not in the category 'Explosives'.
- Not in the category 'Light'.
Consider this group from the perspective of the 'Sound' category. This group is a subset of 'Sound'. Are these 'Sounds' only 'Bombs' (among the categories mentioned)? Yes, because this group is in 'Bombs', is in 'Sound', and is specifically stated (by the interpretation of "Exclusively Sound" in context) to be outside 'Explosives' and 'Light'. Therefore, there exists a group of Sound entities that are also Bombs and are exclusively (or only) Bombs among the given categories. This option appears to be directly implied by the interpretation of Statement 2.
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Some Explosives are Lights.
Statement 1 tells us All Explosives are Sound. Statement 3 tells us Some Light are Bombs but not Sound. There is no information provided in the statements that links 'Explosives' and 'Light' in a way that guarantees any overlap. Statement 1 puts Explosives inside Sound, while Statement 3 puts some Light outside Sound. This option is not necessarily true or implied.
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All Sounds are Explosives.
Statement 1 says "All Explosives are Sound". This means the set of Explosives is a subset of the set of Sound. This does not mean that the set of Sound is a subset of the set of Explosives. The converse is not necessarily true. This option contradicts Statement 1 if there are Sounds that are not Explosives (and Statement 2 implies there are Bombs that are Sound but not Explosives, showing there are Sounds that are Bombs, and these Sounds are not Explosives). This is not an implicit assumption.
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Some Bombs are Explosives.
Statement 2 says "Some Bombs are Exclusively Sound". Based on our interpretation, this group of Bombs is Sound and not Explosives. Statement 3 says "Some light are Bombs but not Sound". This group of Bombs is not Sound, and therefore, since all Explosives are Sound (Statement 1), this group of Bombs cannot be Explosives either. While it is possible that *other* Bombs exist that *could* be Explosives, the statements do not require or imply such an overlap. Statement 2 particularly suggests a group of Bombs that are *not* Explosives. This option is not implicitly assumed.
The Implicit Assumption Explained
The statement "Some Bombs are Exclusively Sound" is the key. In the context of logical reasoning problems like this, "Exclusively Sound" typically means belonging to the 'Sound' category and to none of the other categories mentioned (Explosives, Bombs, Light). Therefore, "Some Bombs are Exclusively Sound" means "Some Bombs are Sound AND are not Explosives AND are not Light". This identified group of entities fits the description in option 1: they are part of 'Sound', they are part of 'Bombs', and they are 'only' Bombs among the specified categories (as they are not Explosives and not Light). Hence, option 1, "Some Sounds are only Bombs," is an implicit assumption required for Statement 2 to hold true under this common interpretation.
| Statement / Option | Interpretation |
|---|---|
| Statement 1: All E are S | Every member of E is also a member of S. (E ⊂ S) |
| Statement 2: Some B are Exclusively S | There's a group of B that is in S, and this group is NOT in E and NOT in L. (Bs_excl ⊂ B, Bs_excl ⊂ S, Bs_excl ∩ E = ∅, Bs_excl ∩ L = ∅) |
| Statement 3: Some L are B but not S | There's a group in L that is in B but not in S. (Lb_not_s ⊂ L, Lb_not_s ⊂ B, Lb_not_s ∩ S = ∅) |
| Option 1: Some S are only B | There's a group in S that is in B, and this group is NOT in E and NOT in L. (Sb_only ⊂ S, Sb_only ⊂ B, Sb_only ∩ E = ∅, Sb_only ∩ L = ∅) |
Comparing the interpretation of Statement 2 with Option 1, we see that the group Bs_excl from Statement 2 perfectly matches the description of the group Sb_only in Option 1. Thus, Option 1 is implicit in Statement 2.
Revision Table: Key Concepts in Logic
| Concept | Description | Example (from statements) |
|---|---|---|
| Universal Affirmative (All A are B) | Every member of set A is a member of set B. | All Explosives are Sound. |
| Particular Affirmative (Some A are B) | At least one member of set A is also a member of set B. | Some Light are Bombs. |
| Particular Negative (Some A are not B) | At least one member of set A is not a member of set B. | Some Light are not Sound (from Statement 3). |
| Exclusivity Clause ("Exclusively", "Only") | Often implies belonging to a category and none of the others mentioned in the context. | Some Bombs are Exclusively Sound implies these Bombs are Sound, and not other mentioned categories. |
| Implicit Assumption | A premise that is not explicitly stated but must be true for the conclusion or statement to be valid within its context. | Some Sounds are only Bombs is implied by "Some Bombs are Exclusively Sound". |
Additional Information on Logical Reasoning
Statements and assumption questions test your ability to understand the underlying premises of given statements. You need to identify what is being taken for granted or what must be true for the statements to make sense as presented. In this type of problem, paying close attention to quantifying words like "All", "Some", and qualifying words like "Exclusively" or "Only" is crucial. Often, the interpretation of these specific terms determines the correct implicit assumption. Visual tools like Venn diagrams can also be helpful to represent the relationships between categories described in the statements and check if the options are necessarily true based on these relationships.
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.
