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
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.
