Three 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 oranges are apples. Some oranges are bananas. All bananas are fruits. Conclusions: I. Some fruits are apples. II. Some apples are bananas. III. Some oranges are fruits.
All conclusions follow.
For the given statements, the minimum possible Venn diagram is shown below:
Conclusions:
I. Some fruits are apples → Follows (Since all oranges are apples, some oranges are bananas, and all bananas are fruits. Therefore, since there is some intersection between oranges and bananas that also falls within apples and fruits, some fruits are apples is definitely true)
II. Some apples are bananas → Follows (Since all oranges are apples and some oranges are bananas. Therefore, since there is some intersection of oranges within bananas that falls within apples, some apples are bananas is definitely true)
III. Some oranges are fruits → Follows (Since some oranges are bananas and all bananas are fruits. Therefore, since there is some intersection between oranges and bananas that falls entirely within fruits, some oranges are fruits is definitely true)
∴ Here, all conclusions I, II, and III follow.
Thus, the correct answer is "All conclusions follow".
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.
