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 engineers are footballers.
All cricketers are footballers.
Conclusions:
(I) Some engineers are cricketers.
(II) All footballers are cricketers.
Analyzing the Statements
Let E be the set of engineers, F be the set of footballers, and C be the set of cricketers.
- Statement 1: Some engineers are footballers. This means the intersection of E and F is not empty (\(E \cap F \neq \emptyset\)).
- Statement 2: All cricketers are footballers. This means the set C is a subset of F (\(C \subseteq F\)).
Evaluating Conclusion (I)
Conclusion (I): Some engineers are cricketers. (\(E \cap C \neq \emptyset\))
From Statement 1, we know some engineers are in the footballer set (F). From Statement 2, we know all cricketers (C) are within the footballer set (F). However, the engineers who are footballers might not overlap with the cricketers, even though both groups are within the larger set of footballers. Therefore, we cannot conclude that some engineers must be cricketers.
Example: Imagine 100 footballers. 20 are cricketers (Set C). 30 are engineers who are also footballers (Set \(E \cap F\)). It's possible these 30 engineers are *not* among the 20 cricketers. Thus, Conclusion (I) does not necessarily follow.
Evaluating Conclusion (II)
Conclusion (II): All footballers are cricketers. (\(F \subseteq C\))
Statement 2 explicitly states that All cricketers are footballers (\(C \subseteq F\)). This is the reverse of Conclusion (II). The statement \(C \subseteq F\) does not imply \(F \subseteq C\). There could be footballers who are not cricketers.
Example: If all cricketers are footballers, it doesn't mean every footballer must be a cricketer. There could be many footballers who play other sports or no sport professionally.
Final Determination
Since neither Conclusion (I) nor Conclusion (II) can be logically deduced from the given statements with certainty, neither conclusion follows.
Similar Questions
Consider the given statements true and decide which of the given conclusion(s) logically follow(s) from the statements.
Statements:
1. All reds are yellows.
2. Some yellow are not greens.
Conclusions:
1. Some yellow are reds
2. All yellow are greens
Consider the given statements to be true and decide which of the conclusions logically follow(s) from the given statements.
Statement:
All fruits are trees. Some trees are birds.
Conclusions:
1. Some birds are trees.
2. Some trees are fruits.
Read the given statements and conclusions carefully. You have to take the given statements to be true even if they seem to be at variance from commonly known facts and decide which conclusion(s) logically follow(s) from the given statements.
Statements:
Some cars are bikes.
All bikes are trucks.
Conclusions:
(I) Some trucks are cars.
(II) All trucks are cars.Read the given statements and conclusions carefully. You have to take the given statements to be true even if they seem to be at variance from commonly known facts and decide which conclusion(s) logically follow(s) from the given statements.
Statements:
Some gold are silver.
Some silver are diamonds.
Conclusions:
(I) Some diamonds are gold.
(II) Some silver are gold.Read the given statements and conclusions carefully. You have to take the given statements to be true even if they seem to be at variance from commonly known facts and decide which conclusion(s) logically follow(s) from the given statements.
Statements:
Some bulbs are sands.
All bulbs are candles.
Conclusion:
(I) Some candles are bulbs.
(II) No candle is a sand.
Consider the given statement to be true and decide which of the conclusions logically follows (s) from the statements.
Statements:
Some angels are gods.
All living being are gods.
Conclusions:
1. Some gods are angels.
2. Some living beings are gods.Consider the given statement as true and decide which of the given conclusions can definitely be drawn from the given statements.
Statements:
Dhoni is a good batsman.
Batsman are smart.
Conclusions:
1. All smart people are batsman
2. Dhoni is smart.Given below are two statement, followed by two conclusion, I and II. You have to consider the statement to be true even if they seem to be at variance from commonly known facts. You have to decide which of the given conclusions, if any, follow(s) from the given statements.
Statement 1: No quadrilaterals are polygons.
Statement 2: All polygons are rhombuses.
Conclusion I: Some rhombuses are quadrilaterals.
Conclusion II: Some rhombuses are polygons.Consider the given statement to be true and decide which of the given conclusions can definitely be drawn from the given statements.
Statements:
Some lawyers are females. Some females are mothers.
Conclusion:
1. Some mothers are females.
2. Some lawyers are mothers.Consider the given statements to be true and decide which of the given conclusions can definitely be drawn from the statements.
Statements:
All sharks are fish. No fish is a snake.
Conclusions:
1. No snake is a shark.
2. No shark is a snake.
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.
