Problem 1 - A Complete Resource Book in Mathematics for JEE Main

Question

Which of the following is not a statement? (A) Give me a glass of water. (B) Asia is a continent. (C) The earth revolves round the sun. (D) The number 6 has two prime factors 2,3 .

Step-by-Step Solution

Answer

Option (A) is not a statement; it is a command.

Step 1: Understanding a Statement

In logic, a statement is a declarative sentence that is either true or false but not both. These statements are objective expressions that can be validated with facts.

Step 2: Analyze Option (A)

The sentence 'Give me a glass of water.' is an imperative sentence that gives a command or request. It is not something that can be objectively proven as true or false.

Step 3: Analyze Option (B)

The sentence 'Asia is a continent.' is a declarative sentence, and it is true. This fits the definition of a statement.

Step 4: Analyze Option (C)

The sentence 'The earth revolves round the sun.' is a declarative sentence, and it is true. This qualifies as a statement.

Step 5: Analyze Option (D)

The sentence 'The number 6 has two prime factors 2,3 .' is a declarative sentence, which is true because 2 and 3 are the prime factors of 6. Thus, it is a statement.

Step 6: Determine which is Not a Statement

Since option (A) is not a declarative sentence that can be proven true or false, it is not a statement. All other options (B), (C), and (D) meet the criteria for being statements.

Key Concepts

Logic Statements

In the realm of logical reasoning, a logic statement is foundational. **What is a Logic Statement?** It's essentially a sentence that asserts something factual. The unique aspect of these statements is that they are either true or false, but never both. This true-or-false nature makes them verifiable, laying the groundwork for building logical arguments and reasoning. For example:

• "The sky is blue." - This can be identified as a logic statement because it can be objectively verified as either true or false.

By understanding and identifying logic statements, we can critically evaluate information and discern objective truths in reasoning.

Declarative Sentences

Declarative sentences play a crucial role in forming logic statements. **What Are Declarative Sentences?** These are sentences that state a fact or description. They're different from questions or commands as they provide a clear, direct assertion about a topic. Some features include:

• They end with a period.
• Their primary purpose is to provide information or make an assertion.

For example, the sentence, "Rainbows have seven colors," is declarative because it presents a factual assertion. Learning how to spot declarative sentences helps in distinguishing statements from other sentence types, like questions or requests. This skill is essential for accurate logical analysis.

True or False Expressions

When analyzing logic statements, it's significant to assess their truth value. **What is a True or False Expression?** It refers to the capability of a statement to be evaluated based on its factual accuracy.

• If a statement is in agreement with facts, it is considered 'true.'
• If not, it is labeled 'false.'

This binary nature simplifies complex logical problems, as each statement provides a clear outcome that can be tested or verified. Consider the statement, "The sun rises in the East," which is objectively true. In contrast, "Cats are a type of plant," is false. Understanding true or false expressions in statements enhances reasoning skills, allowing for greater precision in drawing conclusions.