Statements:
(a) All leaders are corrupt.
(b) Some women are leaders.
Conclusions:
I. Some women are corrupt.
II. All those corrupt are women.
Logical Reasoning: Statements & Conclusions Analysis
This problem involves analyzing logical statements to determine which conclusions necessarily follow.
Statement Analysis
- Statement (a): All leaders are corrupt. This means the set of all leaders is a subset of the set of corrupt people. If someone is a leader, they must be corrupt.
- Statement (b): Some women are leaders. This means there is at least one person who is both a woman and a leader. The sets 'Women' and 'Leaders' have a non-empty intersection.
Evaluating Conclusion I: Some women are corrupt
From Statement (b), we know there exist individuals who are both women and leaders. Let's consider one such individual.
According to Statement (a), every leader is corrupt. Therefore, the woman who is a leader must also be corrupt.
This directly leads to the conclusion that at least one woman is corrupt, which matches Conclusion I.
Thus, Conclusion I logically follows.
Evaluating Conclusion II: All those corrupt are women
Statement (a) tells us that all leaders are corrupt, but it doesn't say anything about *all* corrupt people. There might be corrupt people who are not leaders.
Statement (b) only states that *some* women are leaders. It doesn't imply that *all* corrupt people are women.
We cannot conclude from the given statements that the entire set of corrupt people is contained within the set of women. There could be corrupt individuals who are not women.
Thus, Conclusion II does not logically follow.
Final Determination
Based on the analysis, only Conclusion I is a valid deduction from the given statements.
Similar Questions
- Read the given statement(s) 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 statement(s).
Statements:
All Hummingbirds are Storks.
Some Storks are Flamingos.
Conclusions:
I. Some Hummingbirds are Flamingos.
II. No Flamingos are Hummingbirds. - 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 fathers are brothers.
All brothers are sons.
Conclusions:
(I) All fathers are sons.
(II) All brothers are fathers. - Read the given statements and conclusions carefully and decide which of the conclusions logically follow(s) from the statements.
Statements:
(i) All ships are boats.
(ii) All anchors are ships.
Conclusions:
I. All anchors are boats.
II. Some ships are anchors.
III. No anchor is boat.
IV. Some boats are anchors. Read the given statements and decide which of the conclusions given in the options logically follow from the statements.
Statements:
1. All kitchens are bedrooms.
2. No bedroom is a hall.
Read the given statements and decide which of the conclusions given in the options logically follow from the statements.
Statements:
1. All guitars are instruments.
2. All instruments are bagpipes.
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 balls bounce.
All balls vibrate.
Conclusions:
I. Even the balls that do not bounce, vibrate.
II. The balls that do not bounce, do not necessarily vibrate.- 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:
1. Some kiwis are green.
2. Some apples are kiwis.
Conclusions:
1. Some kiwis are yellow.
2. An apple is green. - 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 from the statements.
Statements:
1. All red are white.
2. All white are black.
Conclusions:
1. Some white are red.
2. Some black are red.
3. Some red are not black.
4. All black are white. - 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 eggs are onions.
All onions are blue.
Conclusions:
I. All eggs are blue.
II. All onions are eggs. - In the following question below are given some statements followed by some conclusions based on those statements. Taking the given statements to be true even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which of the given conclusion logically follows the given statements.
Statements:
I. All D are E.
II. Some E are F.
Conclusions:
I. All D are F.
II. Some F are D.
III. Some F are E.
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.
