Question

1. the venn diagram shows the relationship among three sets of numbers. rational numbers integers whole numbers which value would not be located in the shaded region of the diagram? a. $-\frac{8}{2}$ b. $-33$ c. $\frac{11}{8}$ d. 2

Explanation:

Step1: Analyze the shaded region

The shaded region is "Integers" (inside Rational numbers, outside Whole numbers). So we need to find which option is not an integer (or is an integer but in Whole numbers? Wait, no: the shaded region is Integers (the gray part, which is Integers but not Whole numbers? Wait, the Venn diagram: Rational numbers (outer), then Integers (middle, gray), then Whole numbers (inner, white). So shaded region is Integers that are not Whole numbers (since Whole numbers are inside Integers, white). Wait, no: the gray area is Integers (so all integers, including those that are whole numbers? Wait, the diagram: Rational numbers (big rectangle), then inside it, Integers (gray rectangle), then inside Integers, Whole numbers (white rectangle). So the shaded region is Integers (so any integer, because the gray is Integers, which includes Whole numbers? Wait, no, the white is Whole numbers, so the gray is Integers minus Whole numbers? Wait, no, the shading: the middle rectangle (Integers) is gray, and inside it, Whole numbers (white). So the shaded region is Integers (so all integers, because the gray is the Integers set, and Whole numbers are a subset of Integers (white inside gray). Wait, maybe I misread: the shaded region is the Integers (the gray part), which is a subset of Rational numbers, and Whole numbers are a subset of Integers. So the shaded region is Integers (so any integer, including positive integers (Whole numbers) and negative integers and zero? Wait, no: Whole numbers are non-negative integers (0,1,2,...), Integers are ...-2,-1,0,1,2..., so Integers include Whole numbers. So the shaded region is Integers (the gray area), which is all integers. So we need to find which number is not an integer.

Step2: Evaluate each option

• Option A: $-\frac{8}{2} = -4$, which is an integer (negative integer, so part of Integers, and since -4 is not a Whole number (Whole numbers are 0,1,2...), so -4 is in the shaded region (Integers, not Whole numbers? Wait, no: Whole numbers are 0,1,2..., so -4 is an integer (Integers) and not a Whole number, so it's in the shaded region.
• Option B: -33 is an integer (negative integer), not a Whole number, so in shaded region.
• Option C: $\frac{11}{8} = 1.375$, which is a rational number but not an integer. So it's not in the Integers set, hence not in the shaded region (which is Integers).
• Option D: 2 is a Whole number (since Whole numbers are 0,1,2...), and 2 is an integer. But is 2 in the shaded region? The shaded region is Integers (gray), and Whole numbers are inside Integers (white). So 2 is in Whole numbers (white), so is 2 in the shaded region? Wait, the shaded region is the gray part, which is Integers minus Whole numbers? Wait, maybe the diagram: the gray is Integers, and the white is Whole numbers (a subset of Integers). So the shaded region is Integers (so all integers, including those in Whole numbers? But the white is Whole numbers, so the gray is Integers (so 2 is an integer, and part of Whole numbers, but is 2 in the shaded region? Wait, maybe the question is: the shaded region is Integers (so any integer), so we need to find which is not an integer. Let's check each:

A: $-8/2 = -4$ (integer)
B: -33 (integer)
C: 11/8 = 1.375 (not integer)
D: 2 (integer)

So the number that is not an integer is 11/8 (Option C), so it would not be in the shaded region (which is Integers).

Answer:

C. $\frac{11}{8}$