RD Sharma Class 11 Solutions Chapter 31 - Mathematical Reasoning (Ex 31.3) Exercise 31.3 - Free PDF
FAQs on RD Sharma Class 11 Solutions Chapter 31 - Mathematical Reasoning (Ex 31.3) Exercise 31.3
1. What types of problems are primarily covered in the RD Sharma Class 11 Solutions for Chapter 31, Exercise 31.3?
RD Sharma Class 11 Solutions for Exercise 31.3 primarily focus on compound statements. The questions require you to identify the individual component statements that are joined by logical connectives like 'AND' and 'OR'. The main objective is to break down complex statements and analyse their parts, a foundational skill in mathematical reasoning.
2. How do you correctly solve questions from Exercise 31.3 that involve finding component statements?
To correctly solve these problems, follow this step-by-step method:
Step 1: Read the full compound statement provided in the question.
Step 2: Identify the logical connective used, which will typically be 'AND' or 'OR' in this exercise.
Step 3: Write down the simple statements that are being connected. For example, in the statement "The sun is shining and it is warm outside," the component statements are "The sun is shining" and "it is warm outside."
3. Why is understanding the connective 'OR' crucial for determining the validity of a statement in Exercise 31.3?
Understanding the connective 'OR' is crucial because it has a specific meaning in mathematical logic. A compound statement using 'OR' is considered true if at least one of its component statements is true. It is also true if all component statements are true. The only time an 'OR' statement is false is when every single one of its component statements is false. Misinterpreting this can lead to incorrect conclusions about the statement's validity.
4. What is a common mistake students make when determining the truth value of a compound statement using 'AND'?
A common mistake is believing that a compound statement with 'AND' is true if at least one part is true. This is incorrect. For a statement connected by 'AND' to be valid, all of its component statements must be true. If even a single component is false, the entire compound statement becomes false. For example, the statement "A square has four sides and 3 is an even number" is false because the second component is false.
5. How does the method for validating a statement with 'AND' differ from one with 'OR' as per the concepts in Ex 31.3?
The validation methods are fundamentally different based on the connective used:
For 'AND' (Conjunction): The compound statement is true if and only if all of its component statements are true. It requires strict, universal truth.
For 'OR' (Disjunction): The compound statement is true if at least one of its component statements is true. It allows for flexibility and is only false when all components are false.
Understanding this distinction is key to solving problems in Exercise 31.3 and is a core principle of mathematical reasoning.
6. Can a mathematically valid statement in Chapter 31 be composed of sentences that are factually incorrect in the real world?
Yes, absolutely. Mathematical reasoning focuses on the logical structure and the rules of connectives, not necessarily on the factual accuracy of the component statements. For example, the statement "If the moon is made of cheese, then 2+2=4" is a valid implication in logic. The process taught in this chapter helps you determine the logical validity based on assumed truth values, which is a separate concept from real-world verification.
