Three statements are given followed by three conclusions. 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 blacks are blues.
All blues are pinks.
No pink is a green.
Conclusions:
1. All greens can be blues.
2. Some pinks are blacks.
3. All blacks are greens.
Analyzing Syllogism Statements
We are given three statements and need to determine which conclusions logically follow. Let's represent the sets:
- B = Blacks
- Bl = Blues
- P = Pinks
- G = Greens
The statements translate to:
- Statement 1: All blacks are blues. ( $B \subseteq Bl$ )
- Statement 2: All blues are pinks. ( $Bl \subseteq P$ )
- Statement 3: No pink is a green. ( $P \cap G = \emptyset$ )
Deriving Conclusions Logically
From statements 1 and 2, we can deduce that all blacks are pinks:
- Since $B \subseteq Bl$ and $Bl \subseteq P$, it follows that $B \subseteq P$. (All blacks are pinks).
From the deduced conclusion ($B \subseteq P$) and statement 3 ($P \cap G = \emptyset$), we can deduce that no black is green:
- Since all blacks are pinks and no pink is green, it follows that no black is green. ( $B \cap G = \emptyset$ ).
Evaluating Each Conclusion
-
Conclusion 1: All greens can be blues.
- We know $Bl \subseteq P$ (All blues are pinks) and $P \cap G = \emptyset$ (No pink is green).
- Since blues are a subset of pinks, and pinks are completely separate from greens, blues must also be separate from greens.
- Therefore, no green can be blue. This conclusion is false.
-
Conclusion 2: Some pinks are blacks.
- We deduced that $B \subseteq P$ (All blacks are pinks).
- If all members of set B are also members of set P, and assuming set B is not empty, then there must be some members of set P that are also members of set B.
- Therefore, some pinks are blacks. This conclusion is true.
-
Conclusion 3: All blacks are greens.
- We deduced that $B \cap G = \emptyset$ (No blacks are greens).
- This directly contradicts the conclusion that all blacks are greens.
- Therefore, this conclusion is false.
Final Decision
Only conclusion 2 logically follows from the given statements.
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.
