Consider the following three statements:
1. Only students can participate in the race.
2. Some participants in the race are girls.
3. All girl participants in the race are invited for coaching.
Which one of the following conclusions can be drawn from the above statements?
All participants in the race are invited for coaching.
All students are invited for coaching.
All participant in the race are students.
None of the statements (a), (b) and ( c) given above is correct.
This question requires us to draw a logical conclusion from a set of given statements. We will analyze each statement and then evaluate the given options to find the one that logically follows from the premises.
C) All participant in the race are students.
The following two items consists of four statements. Of these four Statements, two cannot both be true, but both can be false. Study the statements carefully and identify the two that satisfy the above condition.
Select the correct answer using the codes given below each set of statements:
Examine the following statements:
1. All animals are carnivorous
2. Some animals are not carnivorous.
3. Animals are not carnivorous.
4. Some animals are carnivorous.
The problem asks us to identify two statements from a given set of four that cannot both be true, but both can be false. This is a classic logic problem involving the relationships between categorical propositions.
Let's analyze each statement:
Now, let's examine the conditions: "cannot both be true, but both can be false." This describes a subcontrary relationship in traditional logic, but more generally, it points to propositions that are contradictory or contrary, with an added condition for falsity.
We are looking for statements that are contrary.
Let's test the pairs:
The pair 1 and 3 ("All animals are carnivorous" and "Animals are not carnivorous") are contrary propositions. They cannot both be true (because if all are, none cannot be), but they can both be false (if some animals are carnivorous and some are not). This perfectly matches the given condition.
Examine the following statements:
1. All trains are run by diesel engine.
2. Some trains are run by diesel engine.
3. No train is run by diesel engine.
4. Some trains are not run by diesel engine.
Which of the above statements are not correct
This question asks us to identify which statements are incorrect based on general knowledge about trains. We need to evaluate each statement individually to determine its factual accuracy.
The question asks for the statements that are not correct.
Therefore, statements 1 and 3 are the incorrect ones.
C) 1 and 3 are the statements that are not correct, as determined by our evaluation.
Examine the following statements:
1. None but the rich can afford air-travel.
2. Some of those who travel by air become sick.
3. Some of those who become sick require treatment.
Which one of the following conclusions can be drawn from the above statements?
All the rich persons travel by air.
Those who travel by air become sick.
All the rich persons become sick.
All those who travel by air are rich.
This is a logical deduction question. We need to analyze each statement carefully and identify the necessary conclusion that logically follows from all given statements. We will use Venn diagrams or set theory concepts to visualize the relationships.
Analyze Statement 1: "None but the rich can afford air-travel."
This statement means that if a person travels by air, they must be rich. It establishes a necessary condition: Air-travelers \(\subseteq\) Rich people. Or, in other words, only rich people are in the set of air-travelers.
Analyze Statement 2: "Some of those who travel by air become sick."
This means there is an intersection between the set of air-travelers and the set of people who become sick. It does not imply that all air-travelers become sick, nor does it imply that all sick people travel by air.
Analyze Statement 3: "Some of those who become sick require treatment."
This means there is an intersection between the set of people who become sick and the set of people who require treatment. It does not imply that all sick people require treatment, nor does it imply anything about air-travelers directly.
Combine the statements to find a conclusion.
The first statement is the most restrictive and provides a direct relationship between "air-travelers" and "rich people". It states that anyone who travels by air must be rich. This is a definitive, universal statement about air-travelers.
D) All those who travel by air are rich. This conclusion directly follows from Statement 1: "None but the rich can afford air-travel." This phrase is equivalent to saying "Only the rich can afford air-travel," which implies that if you are an air-traveler, you must be rich. Therefore, all air-travelers are rich.
A) All the rich persons travel by air. This is incorrect. Statement 1 says that only rich people can afford air travel, but it does not say that all rich people actually travel by air. There might be rich people who choose not to travel by air.
B) Those who travel by air become sick. This is incorrect. Statement 2 says "Some of those who travel by air become sick," not all. "Some" implies that there are also air-travelers who do not become sick.
C) All the rich persons become sick. This is incorrect. We know that some rich people travel by air (from statement 1 and the fact that some people travel by air). We also know that some of those who travel by air become sick (statement 2). However, this does not mean all rich people become sick. The connection is too indirect and not universal for all rich people.
Examine the following statements:
1. All colours are pleasant.
2. Some colours are pleasant.
3. No colour is pleasant.
4. Some colours are not pleasant.
Given that statement 4 is true, what can be definitely concluded?
1 and 2 are true.
3 is true.
2 is false.
1 is false.
This problem involves analyzing the logical relationships between universal and particular statements (affirmative and negative). We are given that statement 4 ("Some colours are not pleasant") is true and need to determine what else can be definitively concluded.
D) 1 is false. If it is true that "Some colours are not pleasant," it logically follows that the statement "All colours are pleasant" cannot be true. These two statements are contradictories in a certain sense, or more precisely, the truth of the particular negative (Some S are not P) directly falsifies the universal affirmative (All S are P).
Consider the following statements followed by two conclusions:
Statements :
Some men are great.
Some men are wise.
Conclusion I : Men are either great or wise.
Conclusion II : Some men are neither great nor wise.
Which one of the following is correct?
Only conclusion I is valid
Only conclusion II is valid
Both the conclusions are valid.
Neither of the conclusions is valid.
This problem involves analyzing logical statements and conclusions. We need to determine if the given conclusions logically follow from the statements. We will use Venn diagrams or basic set theory concepts to visualize the relationships and test the validity of each conclusion.
These statements tell us about the existence of certain men who possess specific qualities (greatness, wisdom). They do not provide information about all men, nor do they specify the relationship between 'great' and 'wise' men.
D) Neither of the conclusions is valid.
