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.
Statements Analysis
We are given two statements about the relationship between anchors, ships, and boats.
- Statement (i): All ships are boats. This can be represented as $Ships \subseteq Boats$.
- Statement (ii): All anchors are ships. This can be represented as $Anchors \subseteq Ships$.
Conclusion Verification
Using the given statements, we can deduce further relationships:
- From $Anchors \subseteq Ships$ and $Ships \subseteq Boats$, by transitivity, we can conclude that All anchors are boats ($Anchors \subseteq Boats$).
- Since $Anchors \subseteq Ships$, this implies that if anchors exist, they are also ships. Therefore, Some ships are anchors is a valid conclusion.
- The conclusion No anchor is boat directly contradicts the derived conclusion that all anchors are boats. Thus, this conclusion does not follow.
- Since $Anchors \subseteq Boats$, this implies that if anchors exist, they are also boats. Therefore, Some boats are anchors is a valid conclusion.
Based on the analysis:
- Conclusion I (All anchors are boats) follows.
- Conclusion II (Some ships are anchors) follows.
- Conclusion III (No anchor is boat) does not follow.
- Conclusion IV (Some boats are anchors) follows.
Therefore, conclusions I, II, and IV logically follow 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 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 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 Wolves are Rhinoceroses.
No Rhinoceroses are Kangaroos.
Conclusions:
I: No Kangaroos are Wolves.
II: Some Kangaroos are Wolves. - 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 doors are carpets.
No carpet is a mat.
Conclusions:
(I) No door is a mat.
(II) No mat is a carpet. - 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.
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.
