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:
Some tapes are glue.
Some glue are paints.
All paints are computers.
Conclusions:
I. Some tapes are paints.
II. All glue are paints.
III. Some glue are computers.
Logical Reasoning: Syllogism Analysis
Statement Analysis
We are given three premises to assume as true:
- Premise 1: Some tapes are glue. (This means there is an overlap between the set of tapes and the set of glue.)
- Premise 2: Some glue are paints. (This means there is an overlap between the set of glue and the set of paints.)
- Premise 3: All paints are computers. (This means the set of paints is entirely contained within the set of computers.)
Conclusion Analysis
Let's evaluate each conclusion based on the premises:
-
Conclusion I: Some tapes are paints.
- From Premise 1, some tapes overlap with glue.
- From Premise 2, some glue overlaps with paints.
- However, the overlap between tapes and glue does not necessarily overlap with paints. There's no guarantee that any tapes are paints.
- Therefore, Conclusion I does not necessarily follow.
-
Conclusion II: All glue are paints.
- Premise 2 explicitly states "Some glue are paints," not all.
- Therefore, Conclusion II contradicts Premise 2 and does not follow.
-
Conclusion III: Some glue are computers.
- From Premise 2, we know that there exists at least one glue that is also a paint (Some glue are paints).
- From Premise 3, we know that every paint is a computer (All paints are computers).
- Therefore, the glue that is a paint must also be a computer. This means some glue are computers.
- Conclusion III logically follows from Premises 2 and 3.
Final Decision
Only Conclusion III logically follows from the given statements. This corresponds to Option 4.
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.
