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Class 11 Applied Maths Chapter 8 Solutions
Logical Reasoning
EXERCISE- 8.2
Q.1 A’s mother is the only daughter of B’s father. If B is female then how B is related to A?
Ans. To determine how B is related to A, we need to analyze the given information:
- A’s mother is the only daughter of B’s father.
- B is female.
Let’s break it down step-by-step:
- A’s mother is the only daughter of B’s father:
- This means A’s mother is the daughter of B’s father.
- Since B is female and we are talking about B’s father, B is also a child of B’s father.
- The only daughter:
- A’s mother is the only daughter of B’s father.
- If A’s mother is the only daughter, then B cannot be another daughter. This implies that B must be the same person as A’s mother (since there cannot be two daughters, and A’s mother is the only daughter).
Therefore, B is A’s mother.
Q.2 Pointing to a man Parul said “He is the only son of my mother-in-law”. How is the man related to Parul?
Ans. To determine the relationship, let’s analyze the information:
- The man is the only son of Parul’s mother-in-law.
Parul’s mother-in-law is her husband’s mother. The only son of Parul’s mother-in-law would be Parul’s husband.
Therefore, the man is Parul’s husband.
Q.3 Pointing to a girl in the photograph, Ajeet said “Her father is the only son of my father”. How is that girl related to Ajeet?
Ans. To determine the relationship, let’s break down the information provided:
- Ajeet says the girl’s father is the only son of Ajeet’s father.
The only son of Ajeet’s father would be Ajeet himself (assuming Ajeet is a male and has no brothers). Therefore, the girl’s father is Ajeet.
This means the girl in the photograph is Ajeet’s daughter.
Therefore, the girl is Ajeet’s daughter.
Q.4 A man looks at a picture and says “Her father’s sister’s son is my younger brother”. How is he related to the person in the picture?
Ans. To determine the relationship, let’s break down the information provided:
- The man says, “Her father’s sister’s son is my younger brother.”
This means:
- The person in the picture is a female (“Her”).
- Her father has a sister.
- The sister has a son who is the man’s younger brother.
The man’s younger brother is the son of the father’s sister, making him the cousin of the girl in the picture. Since the man and his younger brother share the same parents, the man is also the cousin of the girl in the picture.
Therefore, the man is the girl’s cousin.
Q.5 Introducing to a man, a lady said “The father of his brother is the only son of my mother”. How is that man related to the lady?
Ans. To determine the relationship, let’s break down the information provided:
- The lady said, “The father of his brother is the only son of my mother.”
This means:
- “The only son of my mother” refers to the lady’s brother (assuming she has no other brothers).
- “The father of his brother” refers to the man’s father.
Since the lady’s brother is the only son of her mother, the lady’s brother is the man’s father. Therefore, the man must be the lady’s nephew.
So, the man is the lady’s nephew.
Q.6 Arun said, ‘Ishika is the daughter of my mother’s daughter’. How is Arun related to Ishika?
Ans. To determine the relationship, let’s analyze the information provided:
- Arun said, “Ishika is the daughter of my mother’s daughter.”
Arun’s mother’s daughter would be Arun’s sister. So, Ishika is the daughter of Arun’s sister.
Therefore, Ishika is Arun’s niece.
So, Arun is Ishika’s maternal uncle.
Q.7 Pointing to a man Akshay said, ‘His son is my son’s uncle’. How is the man related to Akshay?
Ans. To determine the relationship, let’s analyze the information:
- Akshay says, “His son is my son’s uncle.”
If the man’s son is Akshay’s son’s uncle, this means the man’s son is Akshay’s brother. Therefore, the man is Akshay’s father.
So, the man is Akshay’s father.
Q.8 P is the son of Q and husband of R, who is the sister of S, who is the father of T, who is the brother of U, who is the daughter of V.
(i) How is P related to V?
(iii) How is P related to S?
(ii) How is R related to U?
(iv) How is S related to V?
Ans. Let’s break down the information to determine the relationships:
- Family Relationships:
- P is the son of Q and husband of R.
- R is the sister of S.
- S is the father of T.
- T is the brother of U.
- U is the daughter of V.
- R is the sister of S, so R and S are siblings.
- P is married to R, making P the son-in-law of S.
- S is the father of T and U, so T and U are siblings.
- U is the daughter of V, making S (father of U) the partner of V (since U is their child).
- Determine the Relationships:
- (i) How is P related to V?
- P is married to R, who is S‘s sibling. Since S is the partner of V, P is the son-in-law of V.
- (ii) How is R related to U?
- R is the mother of T and U. Therefore, R is U‘s mother.
- (iii) How is P related to S?
- S is the father of T and U, and P is married to R (S’s sibling). Hence, P is the brother-in-law of S.
- (iv) How is S related to V?
- S is the partner of V (since S and V are the parents of T and U). Thus, S is V‘s partner.
- (i) How is P related to V?
Therefore:
- (i) P is the son-in-law of V.
- (ii) R is U’s mother.
- (iii) P is the brother-in-law of S.
- (iv) S is V’s partner.
Q.9 Read the information given below and answer the questions that follow:
In a family, there are six members P, Q, R, S, T and U. Q is wife of P. S is the only son of R, who is the brother of P. T is the sister of S. Q is the daughter-in-law of U, who is widow. (ii) How T is related to R?
(i) How U is related to P?
(iii) How R is related to Q?
(iv) How S is related to U?
Ans. To determine the answers, let’s analyze the relationships in the family step-by-step:
- Family Relationships:
- Q is the wife of P.
- S is the only son of R, who is the brother of P. This means R is P’s brother, making S R’s son.
- T is the sister of S. Thus, T is also R’s daughter.
- Q is the daughter-in-law of U, who is a widow. Since Q is married to P, and U is a widow, U must be P’s mother.
- Putting it Together:
- U (widow) is P’s mother.
- R is P’s brother, making R’s children S and T.
- Q is P’s wife, thus U is Q’s mother-in-law.
- S and T are the children of R.
- Answering the Questions:
- (i) How is U related to P?
- U is P’s mother.
- (ii) How is T related to R?
- T is R’s daughter.
- (iii) How is R related to Q?
- R is Q’s father-in-law (since R is P’s brother and Q is P’s wife).
- (iv) How is S related to U?
- S is U’s grandson (since S is the son of P, who is U’s child).
- (i) How is U related to P?
Therefore:
- (i) U is P’s mother.
- (ii) T is R’s daughter.
- (iii) R is Q’s father-in-law.
- (iv) S is U’s grandson.
Q.10 Read the information given below and answer the questions that follow:
In a family of 6 members A, B, C, D, E and F. B is daughter-in-law of F. D is grandchild of A C is the only uncle of D. A has two children F and C, one male and one female. E is the father of C.
(i) Who is the mother-in-law of B?
(iii) How D is related to F?
(ii) Who is the grandfather of D?
(iv) How B is related to D?
(v) If a girl G is married into the family, then what will be the relationship between G and E?
Ans. To determine the answers, let’s analyze the relationships and structure of the family:
- Members and Relationships:
- B is the daughter-in-law of F.
- D is the grandchild of A.
- C is the only uncle of D.
- A has two children: F and C (one male and one female).
- E is the father of C.
- Identifying Relationships:
- A has two children: F and C.
- Since F is mentioned as having a daughter-in-law (B), F must be the female child of A.
- C, being the only uncle of D, is the male child of A.
- E is the father of C, which means E is A’s husband.
- B is the daughter-in-law of F, so B is married to F’s son.
- D is the grandchild of A, and since C is the only uncle of D, D must be the child of F.
- A has two children: F and C.
- Putting it All Together:
- A and E are the grandparents.
- C is the uncle of D.
- F is the mother of D.
- B is the wife of F’s son (who is not named explicitly, but must be the father of D).
- Questions Answered:
- (i) Who is the mother-in-law of B?
- F is the mother-in-law of B.
- (ii) Who is the grandfather of D?
- E is the grandfather of D.
- (iii) How is D related to F?
- D is F’s child.
- (iv) How is B related to D?
- B is D’s mother.
- (v) If a girl G is married into the family, then what will be the relationship between G and E?
- If G marries into the family and there are no further details, the most likely scenario is G would be married to C (as C is a male and unmarried in the given context). In this case, G would be E’s daughter-in-law.
- (i) Who is the mother-in-law of B?
Therefore:
- (i) F is the mother-in-law of B.
- (ii) E is the grandfather of D.
- (iii) D is F’s child.
- (iv) B is D’s mother.
- (v) If G is married to C, then G would be E’s daughter-in-law.
Q.11 In a family, there are 7 members P, Q, R, S, T, U and V. P the head of the family is a Lawyer. R and T are brothers and both are doctors. S, the wife of T is a social worker. Q is the son of U, who is daughter-in-law of P. V is the cousin sister of Q. If there are two married couples and a female teacher who is married in the family, answer the following questions:
(i) Who is married to R?
(iii) How T is related to V?
(ii) What is the profession of U?
(iv) How P is related to S?
Ans. To determine the answers, let’s analyze the relationships and professions in the family:
- Members and Relationships:
- P is the head of the family and a lawyer.
- R and T are brothers and both are doctors.
- S is the wife of T and a social worker.
- Q is the son of U.
- U is the daughter-in-law of P.
- V is the cousin sister of Q.
- There are two married couples.
- A female teacher is married in the family.
- Breaking Down the Relationships:
- Since U is the daughter-in-law of P and Q is U’s son, T must be U’s husband (because U’s husband is P’s son and P has only two sons, R and T).
- This makes U the wife of T and a female teacher.
- S is the wife of T, thus, T has two relationships which indicate a misunderstanding. However, to resolve:
- Since S is explicitly stated as the wife of T, U is likely to be R’s wife and a female teacher.
- V is the cousin sister of Q. Since Q is U and T’s son, V must be the daughter of R and his wife (U).
- Questions Answered:
- (i) Who is married to R?
- U is married to R.
- (ii) What is the profession of U?
- U is a teacher.
- (iii) How is T related to V?
- T is V’s uncle (since V is R’s daughter and R is T’s brother).
- (iv) How is P related to S?
- P is S’s father-in-law (since S is married to P’s son T).
- (i) Who is married to R?
Therefore:
- (i) U is married to R.
- (ii) U is a teacher.
- (iii) T is V’s uncle.
- (iv) P is S’s father-in-law.
Q.12 Read the information given below and answer the questions that follow:
In a family, there are 9 members A, B, C, D, E, F, G, Hand I. This family consists of 3 generations and 3 married couples. I is the grandson of A, who is married to a doctor. C is the mother of D. F is the daughter-in-law of C. G, the teacher is the father of H, who is the first cousin of E and L. E is the daughter of F, who is an engineer. D is the sister of B. There is a male lawyer, a female politician and three unmarried students, while the eldest member of the family is retired.
(i) Who is the politician?
(iii) What is the profession of C?
(ii) Who is the lawyer?
(iv) Name the three students.
(v) How many children does the engineer have?
(vi) How A is related to H?
Ans.To determine the answers to the questions, let’s break down the given information and establish relationships within the family:
- Members and Relationships:
- 9 members: A, B, C, D, E, F, G, H, I
- 3 generations and 3 married couples
- I is the grandson of A
- A is married to a doctor
- C is the mother of D
- F is the daughter-in-law of C
- G is the father of H and is a teacher
- H is the first cousin of E and I
- E is the daughter of F and F is an engineer
- D is the sister of B
- There is a male lawyer, a female politician, and three unmarried students
- The eldest member is retired
- Profession and Relationship Identification:
- Since H is the first cousin of E and I, and E is the daughter of F (the engineer), F must be married to D (because D is the sister of B and B is not mentioned as married to F).
- Therefore, C is the mother of D and B.
- F is the daughter-in-law of C, which means F is married to B.
- A is married to C and A is the retired eldest member.
- G (the teacher) is the father of H, making H part of a different immediate family.
- E and I are siblings (since both are first cousins of H).
- I is the grandson of A, so A and C are I’s grandparents.
- The lawyer and politician remain unidentified; hence, the lawyer is likely B (married to F), and the politician is likely D, based on elimination and typical role assignment.
- Questions Answered:
- (i) Who is the politician?
- D is the politician.
- (ii) What is the profession of C?
- C’s profession isn’t explicitly stated, but A (C’s spouse) is retired, and C’s involvement suggests a non-professional role like homemaker (if based on typical puzzle settings).
- (iii) Who is the lawyer?
- B is the lawyer.
- (iv) Name the three students.
- H, E, and I are the three students.
- (v) How many children does the engineer have?
- The engineer (F) has two children: E and I.
- (vi) How is A related to H?
- A is the grandfather of H (since A is the grandfather of E and I, H’s cousins).
- (i) Who is the politician?
Therefore:
- The politician is D.
- The profession of C isn’t explicitly given, but we can infer it as non-professional, possibly homemaker.
- The lawyer is B.
- The three students are H, E, and I.
- The engineer (F) has two children.
- A is the grandfather of H.
FAQ’s related to Class 11 Applied Maths Chapter 8 on Logical Reasoning:
Q.1 What is logical reasoning?
Ans. Logical reasoning refers to the process of using a structured and methodical approach to arrive at a conclusion based on given premises or facts. It involves critical thinking and the ability to see the logical connections between ideas.
Q.2 What are the common mistakes to avoid in logical reasoning?
Ans. Common mistakes include:
- Assuming correlation implies causation.
- Overgeneralizing from insufficient evidence.
- Ignoring counterexamples.
- Misinterpreting logical connectives.
Q.3 What is a Venn diagram?
Ans. A Venn diagram is a graphical way to represent sets and their relationships using circles. It is used in logical reasoning to visually illustrate the logical relationships between different sets.
Q.4 How are Venn diagrams used in logical reasoning?
Ans. Venn diagrams are used to:
- Show logical relationships between different sets.
- Solve problems involving set operations such as union, intersection, and difference.
- Visualize logical propositions and their truth values.
Q.5 Can you give an example of a logical reasoning problem and solution?
Ans. If all dogs are mammals and some pets are dogs, can we conclude that some pets are mammals?
Solution: Yes, because if all dogs are mammals, and some pets are dogs, it logically follows that those pets which are dogs must also be mammals. Therefore, some pets are mammals.
These are a few Frequently Asked Questions relating to Class 11 Applied Maths Chapter 8
In Class 11 Applied Maths chapter 8, you will explore fascinating topics that form the backbone of practical problem-solving techniques. Through clear explanations, illustrative examples, and step-by-step solutions, you’ll grasp complex concepts effortlessly. Whether you’re preparing for exams or simply eager to deepen your mathematical understanding, Class 11 Applied Maths Chapter 8 promises an enriching learning experience that will set you on the path to success. Class 11 Applied Maths Chapter 8, we delve deep into advanced mathematical concepts that are crucial for understanding.
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