Answer and Step-by-step explanation:
Assertion (A): Every integer is a rational number.
Reason (R): An integer is a number with no decimal or fractional part, from the set of negative and positive numbers, including zero.
To determine the validity of the assertion and reason, let's examine the definitions and properties of rational numbers and integers.
An integer is a whole number that can be positive, negative, or zero, such as -3, 0, 1, 5, etc. Integers do not have fractional or decimal parts.
On the other hand, a rational number is a number that can be expressed as the ratio of two integers, where the denominator is not zero. It can be written in the form a/b, where a and b are integers and b is not zero.
Now, let's consider the assertion and reason:
Assertion (A) states that every integer is a rational number. This is true because every integer can be written as itself divided by 1, which is the ratio of two integers. For example, 5 can be written as 5/1, -3 can be written as -3/1, and so on. Therefore, every integer is indeed a rational number.
Reason (R) states that an integer is a number with no decimal or fractional part, from the set of negative and positive numbers, including zero. This is also true because integers do not have fractional or decimal parts and include both positive and negative numbers, as well as zero.
In conclusion, both the assertion and reason are correct. Every integer is indeed a rational number, and an integer is defined as a number with no decimal or fractional part, from the set of negative and positive numbers, including zero.