Let's analyze each statement one by one.
-
Every Rational number is a Natural number.
False. A rational number can be expressed as the ratio of two integers (e.g., \( \frac{1}{2} \)), but not all rational numbers are natural numbers (which are positive integers like 1, 2, 3, ...). -
Every natural number is also an integer.
True. Natural numbers (0 or the set of positive integers) are a subset of integers. Therefore, every natural number is indeed an integer. -
Every Irrational number is also an Integer.
False. Irrational numbers cannot be expressed as a fraction of two integers, such as \( \sqrt{2} \) or \( \pi \). Since integers are whole numbers (positive, negative, or zero) and rational numbers, irrational numbers cannot be integers. -
0.128128128… is an Irrational number.
False. The number 0.128128128… is a repeating decimal, which means it can be expressed as a fraction (in this case, \( \frac{128}{990} \)). Therefore, it is a rational number, not an irrational number.
So the final answers are:
- False
- True
- False
- False