Let X = {x | x is a whole number less than 15}, Y = { x | x is a multiple of 3}, Z = {x | x is a real number greater than or equal to 5.5}. What is ? (1 point) Responses {0, 3, 6, 9, 12} {0, 3, 6, 9, 12} {3, 6, 9, 12, 15} {3, 6, 9, 12, 15} {...,, , 0, 3, 6, 9,...} {..., Image with alt text: negative 6 , Image with alt text: negative 3 , 0, 3, 6, 9,...} {..., , , 0, 3, 6, 9, 12}
The set X consists of all whole numbers less than 15, so X = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}.
The set Y consists of all multiples of 3, so Y = {0, 3, 6, 9, 12}.
The set Z consists of all real numbers greater than or equal to 5.5, so Z = {x | x ≥ 5.5}.
To find the intersection of these sets, we need to find all the elements that are common to both sets X and Y, and also belong to set Z.
The common elements between X and Y are {0, 3, 6, 9, 12}.
However, none of these elements are greater than or equal to 5.5, so the intersection of X, Y, and Z is the empty set, denoted by {}.
Therefore, the correct answer is {}.
To find the intersection (denoted by ∩) of the sets X, Y, and Z, we need to find the elements that are common to all three sets.
X = {x | x is a whole number less than 15} = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}
Y = {x | x is a multiple of 3} = {0, 3, 6, 9, 12}
Z = {x | x is a real number greater than or equal to 5.5} = [5.5, ∞)
Now let's find the intersection:
X ∩ Y = {x | x is a whole number less than 15 and multiple of 3} = {0, 3, 6, 9, 12}
(X ∩ Y) ∩ Z = {x | x is a whole number less than 15, multiple of 3, and greater than or equal to 5.5} = {3, 6, 9, 12}
So the answer is {3, 6, 9, 12}.
To find the intersection of sets X, Y, and Z, we need to find the elements that are common to all three sets.
Set X: {x | x is a whole number less than 15}
Set Y: {x | x is a multiple of 3}
Set Z: {x | x is a real number greater than or equal to 5.5}
First, let's find the elements that satisfy set X. Since X contains whole numbers less than 15, the elements of X are {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}.
Next, let's find the elements that satisfy set Y. Since Y consists of multiples of 3, the elements of Y are {0, 3, 6, 9, 12, ...}.
Lastly, let's find the elements that satisfy set Z. Since Z consists of real numbers greater than or equal to 5.5, the elements of Z are {5.5, 6, 6.2, 7, 8, 9, 10, 11, 12, 13, ...}.
To find the common elements among all three sets, we need to find the elements that exist in all three sets. The common elements are {6, 9, 12}.
Therefore, the answer to the given question is {6, 9, 12}.