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
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.
