Which Venn diagram correctly represents the relationship between rational numbers and irrational numbers? Explain your answer.
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The Venn diagram that correctly represents the relationship between rational numbers and irrational numbers is one where the two sets of numbers are represented as non-overlapping circles. This is because rational and irrational numbers are two distinct types of numbers that do not intersect with each other.
To understand why, it is essential to know the definitions of rational and irrational numbers.
Rational numbers are numbers that can be expressed as a fraction, where the numerator and denominator are both integers. In other words, any number that can be written in the form a/b, where a and b are integers and b is not equal to zero, is a rational number. Examples of rational numbers include 1/2, -3/4, and 7.
On the other hand, irrational numbers are numbers that cannot be expressed as a fraction and do not terminate or repeat in decimal form. These numbers cannot be written as a ratio of two integers. Examples of irrational numbers include √2, π (pi), and e.
Given these definitions, we can see that there are no common elements between the set of rational numbers and the set of irrational numbers in the context of Venn diagrams. This is why the two circles representing rational numbers and irrational numbers should not overlap in the Venn diagram.
To construct the Venn diagram, draw two separate circles representing rational numbers and irrational numbers. Label them accordingly. Since these two sets have no elements in common, they should not overlap or intersect in any way. This visually represents the relationship between these two types of numbers - they are mutually exclusive.