Statements:
All doors are carpets.
No carpet is a mat.
Conclusions:
(I) No door is a mat.
(II) No mat is a carpet.
This question tests the ability to draw logical conclusions from given statements using principles of syllogism.
Analyzing the Statements
Let D represent Doors, C represent Carpets, and M represent Mats.
- Statement 1: All doors are carpets. This can be represented as: $D \subseteq C$. (The set of Doors is a subset of the set of Carpets).
- Statement 2: No carpet is a mat. This means the sets C and M are disjoint: $C \cap M = \emptyset$.
Evaluating Conclusion (I)
Conclusion (I): No door is a mat. ($D \cap M = \emptyset$)
- From Statement 1, we know all doors (D) belong to the set of carpets (C).
- From Statement 2, we know that nothing in the set of carpets (C) belongs to the set of mats (M).
- Since all doors are within the carpet set, and the carpet set is entirely separate from the mat set, it logically follows that no door can be a mat.
- Thus, Conclusion (I) logically follows.
Evaluating Conclusion (II)
Conclusion (II): No mat is a carpet. ($M \cap C = \emptyset$)
- Statement 2 directly states "No carpet is a mat" ($C \cap M = \emptyset$).
- The relationship "No X is Y" is symmetric, meaning it implies "No Y is X".
- Therefore, "No mat is a carpet" ($M \cap C = \emptyset$) is logically equivalent to "No carpet is a mat".
- Thus, Conclusion (II) logically follows.
Final Deduction
Since both Conclusion (I) and Conclusion (II) logically follow from the given statements, the correct option is the one stating that both conclusions are valid.
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. 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 flats are villas.
No villa is an apartment.
Conclusions:
(I) No flat is an apartment.
(II) No apartment is a villa. - 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 pins are bugs.
All pins are cows.
Conclusions:
(I): Some bugs are cows.
(II): All cows are pins. 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 conclusions logically follow(s) from the statement(s).
Statement:
Most students know English language.
Conclusions:
1. Some students know English language.
2. Some students do not know English language.
- Two statements are given below. Decide which of the options logically follow from these statements.
Statement 1 All bags are toys.
Statement 2: Some toys are suitcases. - 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 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 conclusion(s) logically follow(s) from the statements.
Statements: All kiwis are bananas. All bananas are grapes.
Conclusions (I): All kiwis are grapes.
Conclusions (II): Some grapes are bananas. - 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 lipsticks are tabs.
No tab is a kite.
Conclusions:
(I): Some lipsticks are kites.
(II): Some tabs are lipsticks.
Important Questions from Syllogism
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 dancers are talented.
Some girls are dancers.
Conclusions:
I. Some girls are talented.
II. All talented are girls.
III. All girls are talented.
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 directors are actors.
No actor is a producer.
All choreographers are directors.
Conclusions:
I. No choreographer is producer.
II. Some actors are choreographers.
III. No director is a producer.
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:
All lemons are plums.
All plums are dates.
Some dates are mangoes.
Conclusions:
I. Some lemons are mangoes.
II. Some mangoes are plums.
III. All lemons are dates.
IV. Some mangoes are dates.
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 cards are postcards.
Some cards are envelopes.
All envelopes are copies.
Conclusions:
I. Some copies are envelopes.
II. Some postcards are copies.
III. Some cards are copies.
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 employees are tax-payers.
Some employees are farmers.
Some farmers are doctors.
Conclusions:
I. No farmer is a tax-payer.
II. Some farmers are tax-payers.
