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. Conclusions:
Statements:
All flies are insects.
All insects are lasers.
(I) Some lasers are insects.
(II) All flies are lasers.
Statement Breakdown
We are given two statements and two conclusions. Our goal is to determine if the conclusions logically follow from the statements. We must assume the statements are true, even if they seem unusual.
- Statement 1: All flies are insects.
This means that the category 'flies' is entirely contained within the category 'insects'. If something is a fly, it must also be an insect. We can represent this relationship using set notation as: Flies $\subseteq$ Insects.
- Statement 2: All insects are lasers.
This means that the category 'insects' is entirely contained within the category 'lasers'. If something is an insect, it must also be a laser. We can represent this as: Insects $\subseteq$ Lasers.
Logical Deduction for Conclusion (I)
Conclusion (I): Some lasers are insects.
From Statement 2, we know that "All insects are lasers" (Insects $\subseteq$ Lasers). This tells us that every member of the 'insects' group is also a member of the 'lasers' group. Therefore, the group of 'lasers' includes all insects. If we assume there are insects (which is necessary for the first statement to have meaning), then it logically follows that at least some members of the 'lasers' group must be 'insects'. Thus, Conclusion (I) is valid.
Logical Deduction for Conclusion (II)
Conclusion (II): All flies are lasers.
We can combine the information from both statements using logical transitivity:
- Statement 1 implies: Flies $\subseteq$ Insects
- Statement 2 implies: Insects $\subseteq$ Lasers
If the set of flies is a subset of the set of insects, and the set of insects is a subset of the set of lasers, then it must be true that the set of flies is also a subset of the set of lasers.
Symbolically:
Flies $\subseteq$ Insects and Insects $\subseteq$ Lasers $\implies$ Flies $\subseteq$ Lasers.
This directly translates to "All flies are lasers". Therefore, Conclusion (II) is also valid.
Overall Conclusion Validity
Since both Conclusion (I) and Conclusion (II) are logically derived from the given statements, we can conclude that both follow.
Important Questions from Syllogism (Notes)
- Disregard commonly known facts. Which conclusion would follow on the basis of given statements only.
Statement: Some bottles are car. some cars are cycle.
Conclusion:
(I) Some bottles are cycle is a possibility
(II) All bottles are cycle
In light of the above statements, choose the most appropriate answer from the options given below. - 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 canals are rivers.
Some rivers are oceans.
Some oceans are ponds.
Conclusions:
(I) All ponds are rivers.
(II) All oceans are canals. - 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 bananas are apples.
All apples are grapes.
Some grapes are oranges.
Conclusions:
(I) All grapes are bananas.
(II) All oranges are apples. Take the given statements to be true even if they seem to be at variance with commonly known facts. Then decide which of the given conclusions logically follow the given statements.
Statements :
0% chairs are tables.
All computers are chairs.
Some books are tables.
Conclusions :
I. Not a single table is a computer.
II. Some books are not chairs.
Directions: Study the following Bar-chart and the data provided to answer the questions that follow: Sales of 3-different companies selling T-Shirts for the years from 2006 to 2009 are given. How much percentage of sales decreased for Brand X T-shirt in 2009 compared with 2007?
