Question

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): All even numbers are divisible by two.
Reason (R): An even number is defined as a number divisible by two. In the light of the above statements, choose the most appropriate answer from the options given below.

• A. Both (A) and (R) are correct and (R) is the correct explanation of (A).
• B. Both (A) and (R) are correct but (R) is not the correct explanation of (A).
• C. (A) is correct but (R) is not correct.
• D. (A) is not correct but (R) is correct.

Hint:

In assertion-reason questions, first determine the truth of each statement separately, then check whether the reason actually explains the assertion.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
This is an assertion-reason question that tests the understanding of the mathematical definition of an even number.

Step 2: Key Formula or Approach:
A number is even if it can be written as \(2k\), where \(k\) is an integer.

Step 3: Detailed Explanation:

• Assertion (A) states that all even numbers are divisible by two. This is true by definition.

• Reason (R) states that an even number is defined as a number divisible by two. This is also true.

• The reason directly explains why the assertion is true because the assertion is simply a restatement of the definition.

• Examples such as \(4, 8,\) and \(20\) are all divisible by \(2\), and hence they are even numbers.

• Since both statements are correct and the reason fully explains the assertion, the first option must be selected.

Step 4: Final Answer:
(A) Both (A) and (R) are correct and (R) is the correct explanation of (A).