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 conclusion(s) logically follow(s) from the statements.
Statements:
Some vegetables are nuts.
All fruits are nuts.
Conclusions:
(I) Some vegetables are fruits.
(II) All nuts are fruits.
Statement and Conclusion Analysis
We need to determine if the given conclusions logically follow from the statements.
Analyzing the Statements
- Statement 1: Some vegetables are nuts. This means there is at least one vegetable that is also a nut. In set notation, if V represents vegetables and N represents nuts, then $V \cap N \neq \emptyset$.
- Statement 2: All fruits are nuts. This means the entire set of fruits is contained within the set of nuts. If F represents fruits, then $F \subseteq N$.
Evaluating Conclusion (I)
Conclusion I: Some vegetables are fruits. ($V \cap F \neq \emptyset$)
From Statement 1 ($V \cap N \neq \emptyset$) and Statement 2 ($F \subseteq N$), we cannot conclude that some vegetables are fruits. The vegetables that are nuts might be completely separate from the fruits (which are also nuts). The statements do not provide enough information to link vegetables directly to fruits.
Evaluating Conclusion (II)
Conclusion II: All nuts are fruits. ($N \subseteq F$)
Statement 2 states that all fruits are nuts ($F \subseteq N$). This is not the same as saying all nuts are fruits. It is possible for the set of nuts to be larger than the set of fruits, meaning there could be nuts that are not fruits. Therefore, this conclusion does not logically follow.
Final Determination
Since neither Conclusion (I) nor Conclusion II can be logically deduced from the given statements, the correct option is that neither conclusion follows.
Important Questions from Syllogism (Notes)
- Disregard commonly known facts. Which conclusion would follow on the basis of given statements only.
Statement: Some bottles are car. some cars are cycle.
Conclusion:
(I) Some bottles are cycle is a possibility
(II) All bottles are cycle
In light of the above statements, choose the most appropriate answer from the options given below. - 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 canals are rivers.
Some rivers are oceans.
Some oceans are ponds.
Conclusions:
(I) All ponds are rivers.
(II) All oceans are canals. - 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 bananas are apples.
All apples are grapes.
Some grapes are oranges.
Conclusions:
(I) All grapes are bananas.
(II) All oranges are apples. Take the given statements to be true even if they seem to be at variance with commonly known facts. Then decide which of the given conclusions logically follow the given statements.
Statements :
0% chairs are tables.
All computers are chairs.
Some books are tables.
Conclusions :
I. Not a single table is a computer.
II. Some books are not chairs.
Directions: Study the following Bar-chart and the data provided to answer the questions that follow: Sales of 3-different companies selling T-Shirts for the years from 2006 to 2009 are given. How much percentage of sales decreased for Brand X T-shirt in 2009 compared with 2007?
