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Question
The Venn diagram represents the relationship among whole numbers, rational numbers, irrational numbers, natural numbers, real numbers, and integers.
Drag the names for the sets of numbers to the boxes labeled A, B, C, D, E, and F to correctly label sets A, B, C, D, E, and F in the Venn diagram.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
A B C D E F
A: Natural Numbers
B: Whole Numbers
C: Integers
D: Rational Numbers
E: Irrational Numbers
F: Real Numbers
To correctly label the sets A, B, C, D, E, and F in the Venn diagram, you need to identify which sets of numbers correspond to each label. Here is the correct mapping:
A: Natural numbers (also known as counting numbers) - Set of all positive whole numbers excluding zero (1, 2, 3, ...)
B: Whole numbers - Set of all positive whole numbers including zero (0, 1, 2, 3, ...)
C: Integers - Set of all positive and negative whole numbers including zero (... -3, -2, -1, 0, 1, 2, 3, ...)
D: Rational numbers - Set of all numbers that can be expressed as a ratio of two integers (includes fractions and terminating or repeating decimals)
E: Irrational numbers - Set of all numbers that cannot be expressed as a ratio of two integers (includes non-repeating, non-terminating decimals like π or √2)
F: Real numbers - Set of all rational and irrational numbers
Based on this information, you can place the labels Natural numbers, Whole numbers, Integers, Rational numbers, Irrational numbers, and Real numbers in the Venn diagram accordingly.
To correctly label the sets in the Venn diagram, we need to identify the characteristics of each set of numbers. Here is a breakdown of each set:
A: Natural numbers (also known as counting numbers) are the set of positive integers starting from 1 and continuing infinitely. So, we can drag "Natural numbers" to box A.
B: Whole numbers are the set of natural numbers including zero. So, we can drag "Whole numbers" to box B.
C: Integers are the set of whole numbers and their negatives, including zero. So, we can drag "Integers" to box C.
D: Rational numbers are numbers that can be expressed as a fraction, where the numerator and denominator are both integers (except for dividing by zero). So, we can drag "Rational numbers" to box D.
E: Irrational numbers are numbers that cannot be expressed as a fraction and their decimal representation continues infinitely without repeating. Examples include √2 and π. So, we can drag "Irrational numbers" to box E.
F: Real numbers are the set of all rational and irrational numbers combined. In other words, it includes all numbers on the number line. So, we can drag "Real numbers" to box F.
By correctly labeling each box with the respective set of numbers, we have completed the Venn diagram.