Problem 1 - A Complete Resource Book in Mathematics for JEE Main 2017

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.

Step 1: Define the Concept of a Statement

In logic, a statement is a declarative sentence that is either true or false but not both. It must clearly express a fact, an assertion, or a questionable fact that has a definitive truth value.

Step 2: Analyze Option A

Option A, "Give me a glass of water," is an imperative sentence. It does not declare anything that can be judged as true or false. Instead, it's a command or request.

Step 3: Analyze Option B

Option B, "Asia is a continent," is a declarative sentence stating a fact. It has a truth value since it can be determined true because Asia is indeed a continent.

Step 4: Analyze Option C

Option C, "The earth revolves round the sun," is also a declarative sentence that can be judged as true. It is a well-known scientific fact, so it holds a truth value.

Step 5: Analyze Option D

Option D, "The number 6 has two prime factors 2,3," is another declarative sentence that can be deemed true or false. The statement indeed can be proven true, as 6 is a product of 2 and 3, which are both prime.

Step 6: Identify the Non-Statement

Among the given options, only Option A is not a statement because it does not declare anything with a true or false value. It's a command, not a factual claim.

Key Concepts

Imperative Sentence

An imperative sentence is a type of sentence that gives a command or makes a request. It's a way people express their wants or needs by telling others what to do. When you say, "Close the door," it is an imperative sentence, because it instructs someone to take action. Here are some key characteristics of imperative sentences:

• They typically do not state facts or information.
• They do not have a truth value, as they cannot be proven true or false.
• They often begin with the base form of a verb, often omitting the subject.

Imperative sentences can be very direct, such as in orders, or they can be more polite, as in requests. In logic, because imperative sentences don't express factual information or assertions, they aren't considered "statements" in the true sense, since they lack a truth value.

Declarative Sentence

A declarative sentence is a sentence that makes a statement, providing information, stating a fact, or expressing an assertion. They form the basic building block of logical statements in logical reasoning and problem solving. Consider the sentence "The sky is blue." This is a classic example of a declarative sentence because it conveys information and can be evaluated as true or false.

• Declarative sentences can be verified or disproven, contributing to their truth value.
• They are usually straightforward and end with a period.
• They form the basis of logical statements used in scientific, mathematical, and everyday contexts.

In logic, a sentence like "The earth revolves round the sun" is considered declarative because it states a known fact, and it can be evaluated as true, which gives it a truth value.

Truth Value

The concept of truth value is central to logic. It refers to the truthfulness or falsehood of a statement. In logical terms, a statement must be either true or false, but not both. Truth value is what separates logical statements from other types of sentences, such as imperatives or questions, as those cannot be assigned a truth value.

• In logic, statements like "Asia is a continent" have a truth value because they can be verified; in this case, the statement is true.
• Truth value is essential for logical reasoning, as it allows for the evaluation of statements and the formation of arguments or conclusions.
• Only declarative sentences have truth values, as they convey clear information or claims that can be judged as true or false.

Understanding truth value helps in distinguishing statements in logic exercises, such as determining which sentences can be considered statements. For example, sentences that present factual information or assertions have a truth value, making them core to logic analysis and assessment.