Class 11 Chapter 31 - Mathematical Reasoning (Ex 31.1) RD Sharma Solutions Free PDF
FAQs on RD Sharma Class 11 Solutions Chapter 31 - Mathematical Reasoning (Ex 31.1) Exercise 31.1
1. How can Vedantu's RD Sharma Solutions for Ex 31.1 help me solve Mathematical Reasoning problems?
Vedantu's solutions provide a step-by-step methodology for each problem in Exercise 31.1. They help you understand how to first identify if a sentence is a mathematically acceptable statement and then how to apply logical rules, such as negation, to arrive at the correct answer as per the CBSE 2025-26 syllabus.
2. What is the correct method to determine if a sentence is a statement in Exercise 31.1?
The correct method is to check if the sentence can be definitively judged as either true or false, but not both. For example, "The sum of 2 and 3 is 5" is a true statement. However, a question ("What is your name?"), a command ("Open the door"), or an exclamatory sentence are not statements because they cannot be assigned a truth value.
3. How do I correctly write the negation of a statement as required in RD Sharma Chapter 31?
To write the negation, you must deny the original statement. The simplest way is to insert the word "not" in an appropriate place or to start the sentence with "It is false that...". For example, the negation of "New Delhi is the capital of India" is "New Delhi is not the capital of India". Our solutions demonstrate the precise phrasing for various types of statements.
4. Are there any common mistakes to avoid when solving problems from Exercise 31.1?
Yes, a common mistake is confusing a question or a command with a statement. Only sentences that can be declared true or false are statements. Another pitfall is incorrectly negating statements that contain quantifiers like "all" or "some". For example, the negation of "All dogs are mammals" is not "All dogs are not mammals," but rather "There exists at least one dog that is not a mammal."
5. Why is a sentence with a variable, like "x is a prime number," not considered a statement in the context of this chapter?
A sentence containing a variable is called an open sentence, not a statement, because its truth value depends on the specific value assigned to the variable 'x'. It is neither definitively true nor false on its own. For it to become a statement, the variable must be replaced by a constant. For example, if x = 5, the statement is true. If x = 4, it is false.
6. How does understanding quantifiers like "For all" and "There exists" change the approach to validating statements in Mathematical Reasoning?
Understanding quantifiers is crucial as they define a statement's scope. The approach to validation changes significantly:
- A statement with "For all" (universal quantifier) is proven false if you can find even a single counter-example.
- A statement with "There exists" (existential quantifier) is proven true if you can find just one example that satisfies the condition.
7. The solutions for Ex 31.1 seem straightforward. What is the core skill being developed here for more advanced mathematics?
Exercise 31.1 builds the foundational skill of precision in mathematical language and logical deduction. While identifying statements or writing negations may seem basic, this process trains your brain to think in terms of rigorous, unambiguous logic. This skill is the bedrock for constructing and deconstructing complex proofs in higher-level topics like Calculus, Relations and Functions, and Set Theory.
