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 drinks are shakes.
All teas are shakes.
All shakes are coffee.
Conclusions:
I. All coffees are teas.
II. All coffees are drinks.
III. Some coffees are shakes.
Statements Analysis
The problem presents three statements and three conclusions. We assume the statements are true and evaluate the conclusions based on them. The statements can be represented using set notation:
- All drinks are shakes: $D \subseteq S$
- All teas are shakes: $T \subseteq S$
- All shakes are coffee: $S \subseteq C$
Conclusions Evaluation
We will now assess each conclusion:
Conclusion I: All coffees are teas.
From the statements, we know $T \subseteq S$ and $S \subseteq C$. This implies $T \subseteq C$ (All teas are coffee). However, the statements do not provide information to conclude that $C \subseteq T$ (All coffees are teas). It is possible for coffees to exist that are not teas.
Therefore, Conclusion I does not logically follow.
Conclusion II: All coffees are drinks.
Similarly, we know $D \subseteq S$ and $S \subseteq C$. This implies $D \subseteq C$ (All drinks are coffee). The statements do not support the conclusion $C \subseteq D$ (All coffees are drinks). Coffees might exist that are not drinks.
Therefore, Conclusion II does not logically follow.
Conclusion III: Some coffees are shakes.
The statement $All shakes are coffee$ ($S \subseteq C$) directly means that every item in the category 'shakes' is also in the category 'coffee'. If there is at least one shake, then that shake is a coffee. This confirms that the intersection of coffees and shakes is non-empty.
Therefore, Conclusion III logically follows.
Final Deduction
Based on the logical analysis of the statements, only Conclusion III is valid.
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.
