Which statement is false?
A. The number zero is a rational number.
B. Some irrational are also rational numbers.
C. Every irrational number is a real number.
D. Every integer is a rational number
Is the answer C?
c
a
c
b
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To determine which statement is false, let's analyze each statement:
A. The number zero is a rational number.
Zero is considered a rational number because it can be expressed as the fraction 0/1 or any other fraction where the numerator is zero. Therefore, statement A is true.
B. Some irrational numbers are also rational numbers.
This statement is true. There are indeed some numbers that can be both rational and irrational. For example, the square root of 4 is both a rational number (equal to 2) and an irrational number (since it cannot be expressed as a fraction).
C. Every irrational number is a real number.
This statement is true. All irrational numbers, by definition, exist on the real number line. Therefore, statement C is true.
D. Every integer is a rational number.
This statement is false. While it is true that integers can be expressed as fractions (e.g., 3 can be expressed as 3/1), not all integers can be expressed as fractions with a non-zero denominator. For example, the number π cannot be expressed as a fraction, so it is irrational, not rational.
Based on this analysis, the false statement is D, which means your answer is incorrect.