which statement is false?
a.every integer is a real number.
b.every real number is a rational number.
c. every positive rational number has a square root.
d.every integer is a rational number.
Can an irrational number be a real number? (Yes)
Therefore, B is false because being a real number does not imply being a rational number
Well, well, well, it's time for a ticklish logic question! Let me put on my funny hat and address this one:
The false statement here, my friend, is "b. every real number is a rational number." Why? Because there are some real numbers that just can't be expressed as a fraction. They are called "irrational," and they can make things a bit complicated. Irrational numbers, like pi or the square root of 2, can't be written as a simple fraction or ratio. Tricky, huh?
The statement that is false is:
b. Every real number is a rational number.
Explanation: This statement is false because there are real numbers that cannot be expressed as a fraction of two integers (i.e. irrational numbers), such as the square root of 2 or pi.
To determine which statement is false, let's analyze each option one by one:
a. Every integer is a real number.
This statement is true. Integers are a subset of real numbers. Every whole number, negative whole number, and zero is considered an integer, and these numbers are also real numbers.
b. Every real number is a rational number.
This statement is false. Not every real number is a rational number. Rational numbers are numbers that can be expressed as a fraction (ratio) of two integers. However, there are real numbers that cannot be expressed as a fraction, such as √2 and π. These are known as irrational numbers.
c. Every positive rational number has a square root.
This statement is true. Every positive rational number has a square root that is also a rational number. For example, the square root of 4 is 2, and the square root of 1/4 is 1/2. These square roots are rational numbers.
d. Every integer is a rational number.
This statement is true. Every integer is a rational number because integers can be expressed as a fraction with a denominator of 1. For instance, the integer 5 can be expressed as the fraction 5/1.
In conclusion, the false statement is b. Every real number is a rational number.