Which statment is false?
A. The number zero is a rational number.
B. Some irrational numbers are also rational numbers.
C. Every irrational number is a real number
D. Every integer is a rational number
Is the answer C?
Nope. all irrationals are real.
It's gotta be B. How can a number be rational and irrational (which means NOT rational)?
c
a
c
b
To determine which statement is false, let's examine each option:
A. The statement "The number zero is a rational number" is true since zero can be expressed as the ratio of two integers (0/1, for example).
B. The statement "Some irrational numbers are also rational numbers" is true. For instance, the square root of 4 is both rational (as it can be expressed as the ratio of two integers, 2/1) and irrational (as it cannot be expressed as a finite or repeating decimal).
C. The statement "Every irrational number is a real number" is true. All irrational numbers, which cannot be expressed as fractions or terminating decimals, are indeed real numbers.
D. The statement "Every integer is a rational number" is false. While integers are indeed real numbers, not all of them can be expressed as a ratio of two integers. For example, the square root of 2 is an irrational number, and therefore not a rational number.
Therefore, the false statement is option D.