Free PDF download of RD Sharma Class 11 Solutions Chapter 31 - Mathematical Reasoning
FAQs on RD Sharma Class 11 Solutions Chapter 31 - Mathematical Reasoning (Ex 31.6) Exercise 31.6 - Free PDF
1. What are the key concepts I need to master for solving questions in RD Sharma Class 11 Maths, Exercise 31.6?
For Exercise 31.6 of Chapter 31, Mathematical Reasoning, the primary focus is on quantifiers. You must have a clear understanding of the two main types:
Universal Quantifiers: Represented by phrases like “For all” or “For every”.
Existential Quantifiers: Represented by phrases like “There exists” or “For some”.
The solutions for this exercise demonstrate how to identify these quantifiers in a statement and check its validity.
2. How do the RD Sharma solutions help in solving problems related to the negation of quantified statements?
The solutions provide a step-by-step method for negating statements containing quantifiers, which is a common point of confusion. The key principle illustrated is that when you negate a quantified statement, you must change the quantifier and negate the predicate. For example:
The negation of “For all x, P(x) is true” becomes “There exists an x such that P(x) is not true”.
The negation of “There exists an x such that Q(x) is true” becomes “For all x, Q(x) is not true”.
Following these solved examples helps prevent common errors.
3. Are the methods in RD Sharma Class 11 Solutions for Mathematical Reasoning aligned with the CBSE 2025-26 syllabus?
Yes, the concepts and problem-solving techniques in RD Sharma's Chapter 31 are fully aligned with the Class 11 Maths syllabus for the 2025-26 session. The chapter covers fundamental logical principles, including statements, logical connectives, and quantifiers, which are integral to the CBSE curriculum. These solutions offer supplementary practice that strengthens your understanding of the NCERT topics.
4. What is a common mistake to avoid when checking the validity of a statement in Exercise 31.6?
A common mistake is failing to find a counterexample. For a “For all” statement to be true, it must hold for every single case in its domain. To prove it false, you only need to find one counterexample. Conversely, for a “There exists” statement to be true, you only need to find one single case that satisfies the condition. The solutions for Ex 31.6 repeatedly demonstrate this process of validation and invalidation.
5. How does understanding quantifiers in Exercise 31.6 help in other areas of mathematics?
Understanding quantifiers is crucial beyond this chapter as it forms the basis of logical proof and definition in higher mathematics. Concepts in calculus (like the definition of limits), set theory, and relations and functions rely heavily on precise statements using “For all” and “There exists”. Mastering them here builds a strong foundation for future, more complex topics.
6. Why are there different types of statements like converse, inverse, and contrapositive discussed in this chapter?
Converse, inverse, and contrapositive are transformations of a conditional statement (“if p, then q”). They are crucial in mathematical reasoning because they help analyse the logical relationship between the original statement and its variations. For instance, a statement and its contrapositive are always logically equivalent (if one is true, the other is true). However, a statement is not logically equivalent to its converse or inverse. The RD Sharma solutions illustrate how to correctly formulate each type for a given conditional statement.
7. How many exercises are there in RD Sharma's Class 11 Chapter on Mathematical Reasoning?
The Class 11 Maths chapter on Mathematical Reasoning in the RD Sharma textbook contains a total of 6 exercises. These exercises are structured to build your understanding progressively, starting with basic statements and moving towards more complex topics like logical connectives, implications, and quantifiers, with Exercise 31.6 focusing specifically on the application of quantifiers.
