Statements:
(i) All girls in my class are good dancers.
(ii) All good dancers are acrobats.
(iii) Some boys in my class are acrobats.
Conclusions:
(i) Some boys in my class are good dancers.
(ii) All acrobats in my class are good dancers.
(iii) All girls in my class are acrobats.
Evaluating Logical Conclusions from Statements
This question requires evaluating the logical validity of three conclusions based on three given statements. We need to determine which conclusions necessarily follow from the information provided.
Statements Analysis
Let's represent the statements using logical notation:
- Statement (i): All girls in my class are good dancers. (All G are D)
- Statement (ii): All good dancers are acrobats. (All D are A)
- Statement (iii): Some boys in my class are acrobats. (Some B are A)
Conclusions Evaluation
Now, let's evaluate each conclusion:
-
Conclusion (i): Some boys in my class are good dancers. (Some B are D)
- From Statement (iii), we know Some B are A.
- From Statement (ii), we know All D are A.
- We do not have information linking 'Boys' (B) directly to 'Good Dancers' (D). The set of 'Acrobats' (A) might include individuals who are not 'Good Dancers' (D). Therefore, knowing some boys are acrobats does not guarantee they are good dancers.
- Conclusion (i) does not follow.
-
Conclusion (ii): All acrobats in my class are good dancers. (All A are D)
- Statement (ii) states All D are A.
- Conclusion (ii) is the converse of Statement (ii). The converse is not necessarily true. Just because all good dancers are acrobats, it doesn't mean all acrobats must be good dancers.
- Conclusion (ii) does not follow.
-
Conclusion (iii): All girls in my class are acrobats. (All G are A)
- Statement (i): All G are D
- Statement (ii): All D are A
- Combining these two statements using syllogistic logic (transitivity), if all members of set G are in set D, and all members of set D are in set A, then it must be true that all members of set G are in set A.
- Conclusion (iii) logically follows from Statements (i) and (ii).
Final Deduction
Based on the analysis, only Conclusion (iii) logically follows from the given statements.
Similar Questions
- Read the given statements and conclusions carefully and decide which of the conclusions logically follow(s) from the statements.
Statements:
(i) All the clothes sold in my boutique are of high standard.
(ii) None of the brands except Cara and Cucci are sold at my boutique.
(iii) Some Cucci accessories like bags and makeup are also sold.
Conclusions:
(i) My boutique sells clothes and accessories.
(ii) Cara and Cucci brands have clothes of high standard.
(iii) Some of the accessories sold at my boutique are of Cucci. Read the following statements to answer the given question:
1. All mangoes are sweet.
2. Some apples are sweet.
3. All circular fruits are sweet.
4. Jenny is eating a sweet fruit.
Which of the following inferences is definitely true?
Read the given statement carefully and answer the question: "Inflation is defined as a situation in which more money fetches fewer goods; this makes prices rise and the purchasing power of money fall. Therefore, one is forced to spend more money for the same level of consumption." According to the given statement, which of the following is correct?
Important Questions from Statements and Inferences
Yoga has become a very popular exercise today. But before one joins a yoga class, he/she needs to examine the kind of fitness routine that he/she expects. If one is looking for a high energy, fast-paced aerobic workout, a yoga class might not be the best choice. The statement that best supports this paragraph is
An honest king decided to give death penalty to his minister for some mistake. But he gave him two options: "If you tell correctly what I am thinking now, you will be hanged. But if your guess is wrong, you will be killed by throwing to crocodiles". The clever minister made a statement such that the king could not kill him. The statement made by the minister is
Sita is a twelve year old girl. For many years, she has been asking her parents for a pet dog. Her parents told her that a dog would not be happy in an apartment, but they have given her permission to have a bird. Sita has not yet decided what kind of bird she would like to have. The statement that best supports this paragraph is
Two person S and M have made the following statement among themselves
S say that I am certainly not over 40 year.
M says that I am 38 years and you are at least 5 years older than me.
S says you are at least 39 years.
If all the above statements are wrong, what are the ages of M and S?
- Find the statement that must be true according to the given information.: Erin is twelve years old. For three years, she has been asking her parents for a dog. Her parents have told her that they believe a dog would not be happy in an apartment, but they have given her permission to have a bird. Erin has not yet decided what kind of bird she would like to have.
