Three statements are given, followed by Two conclusions numbered I and II. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements. Statements: Some fractions are marts. No mart is a stud. All studs are frogs. Conclusions: I. Some fractions are definitely not studs. II. Some fractions are definitely not marts.
Logical Analysis of Statements and Conclusions
This problem involves analyzing given statements to determine the validity of logical conclusions. We are asked to assume the statements are true, even if they seem unusual, and apply deductive reasoning.
Understanding the Statements
- Statement 1: Some fractions are marts. (This means there's an overlap between the group 'fractions' and the group 'marts'. At least one fraction is a mart.)
- Statement 2: No mart is a stud. (This indicates that the groups 'marts' and 'studs' are completely separate. Nothing can be both a mart and a stud.)
- Statement 3: All studs are frogs. (This means the entire group 'studs' is included within the larger group 'frogs'.)
Evaluating Conclusion I: Some fractions are definitely not studs
Let's trace the logic:
- Statement 1 tells us that there exist things that are both 'fractions' and 'marts'.
- Statement 2 tells us that anything that is a 'mart' cannot be a 'stud'.
- Therefore, the specific fractions mentioned in Statement 1 (the ones that are also 'marts') cannot possibly be 'studs'.
- This confirms that at least some 'fractions' (those which are 'marts') are definitely not 'studs'.
Conclusion I logically follows from Statements 1 and 2.
Evaluating Conclusion II: Some fractions are definitely not marts
Here's why this conclusion is uncertain:
- Statement 1 ("Some fractions are marts") only guarantees that *at least one* fraction is a mart.
- It does not exclude the possibility that *all* fractions might be marts. The statement "Some A are B" is true even if all A are B.
- If it were true that all fractions were marts, then the conclusion "Some fractions are definitely not marts" would be false.
- Since we can conceive of a situation (all fractions are marts) that is consistent with Statement 1 but makes Conclusion II false, we cannot be certain that Conclusion II logically follows.
Conclusion II does not necessarily follow from the given statements.
Final Determination
Based on the logical analysis, only Conclusion I is guaranteed to be true given the statements. Therefore, only Conclusion I follows.
Similar Questions
- In this question, three statements are given, followed by two conclusions numbered I and II. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follows/follow from the statements.
Statements:
I. Some tables are chairs.
II. All desks are chairs.
III. No chair is a fan.
Conclusions:
I. Some desks are tables.
II. Some fans are desks. - In this question, three statements are given, followed by two conclusions numbered I and II. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follows/follow from the statements.
Statements:
I. All tables are charts.
II. Some charts are graphs.
III. Some graphs are pies.
Conclusions:
I. No table is a graph.
II. Some pies are charts. - In this question, three statements are given, followed by two conclusions numbered I and II. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follows/follow from the statements.
Statements:
All boxes are squares.
All squares are rectangles.
All rectangles are figures.
Conclusions:
I. All boxes are figures.
II. All squares are figures. 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 calculators are lanterns.
Some lanterns are mobiles.
Conclusions:
I. All mobiles are calculators.
II. No mobile is a lantern.
III. Some mobiles are lanterns.
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 parrots are crows.
All crows are eagles.
Conclusions:
I. All parrots are eagles.
Il. Some crows are parrots.
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:
No certificate is a paper.
All pens are papers.
Conclusions:
I. No certificate is a pen.
II. No paper is a certificate.
III. Some papers are pens.
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 officers are clerks.
All clerks are workers.
Conclusions:
I. Some workers are officers.
Il. No worker is an officer.
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 chargers are phones.
No phone is a watch.
Conclusions:
I. All phones are chargers.
Il. No charger is a watch.
Ill. No watch is a phone.
Two statements are given, followed by three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
All wallets are bags.
Some bags are envelopes.
Conclusions:
I. Some wallets are envelopes.
II. No wallet is an envelope.
III. No bag is an envelope.Two statements are given, followed by three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
Some boys are brave.
All boys are punctual.
Conclusions:
I. Some brave are boys.
II. Some punctual are boys.
III. Some brave are punctual.
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:
Some students are players.
All players are male.
Conclusions:
I. All males are players.
II. Some males are students.
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:
No creative is an employer.
All experts are creative.
All workers are experts.
Conclusions:
I. No employer is an expert.
II. No worker is an employer.
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 actors are choreographers.
All choreographers are producers.
Not a single producer is a director.
Conclusions:
I. Some actors are directors.
II. Not a single actor is a director.
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 :
1. All flowers are tulips.
2. No tulips are whites.
Conclusions :
I. All tulips are flowers.
II. Some tulips are whites.
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 rats are dogs.
Some rats are hens.
Conclusions:
I. Some rats are dogs.
II. Some hens are rats.
