Select all of the following true statements if R = real numbers, I = integers, and W = {0, 1, 2, ...}.

Mathematics

1 answer:

Vinvika [58]4 years ago

4 0

Answer and Step-by-step explanation:

We will begin to solve this problem by defining first what the sets' elements really are.

R consists of real numbers. This means that this set contains all the numbers, rational or not.

Z is composed of whole numbers. Integers include all negative and positive numbers as well as zero (it's basically a set of whole numbers and their negated values).

W, on the other hand, has 0,1,2, and its elements are onward. Those numbers are referred to as whole numbers.

W ⊂ Z is TRUE. Z contains all the numbers as stated earlier, and W is a subset of it.

R ⊂ W is FALSE. Not all numbers are complete numbers. Complete numbers must be rational and represented fractionless. These requirements are not met by those real numbers.

0 ∈ Z is TRUE. Zero is just an integer so it is a component of Z.

∅ ⊂ R is TRUE. A set i.e null be R subset, and each and every set is a general set. Moreover, there were not single elements in a null set, so it spontaneous became a non empty set subset through description as there is no element of R.

{0,1,2,...} ⊆ W is TRUE. The set on the left is precisely what is specified in the statement for problem for W. (The bar below the subset symbol simply implies that the subset is not rigid, because the set on the left may be equal to the set on the right. Without it, the argument would be incorrect, because a strict subset needs that the two sets not be identical).

-2 ∈ W is FALSE. W's only made up of whole numbers and not their negated equivalents.

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can someone help me understand this, please? For some reason my answer is correct but I need to understand how did I found the c

Morgarella [4.7K]

Answer with step-by-step explanation:

The way the question is worded, this actually shouldn't be correct. The correct answer should be $3:4$ .

Because the trapezoids are similar, we can find the ratio of their perimeters by actually just finding the ratio of their sides.

Why?

By definition, the corresponding sides of a polygon are in a constant proportion. The perimeter is simply the sum of all sides of the polygon. Since we're just adding the sides, the proportion will still be maintained.

Therefore, we'll just need to ratio of their corresponding sides. The only two corresponding sides that are marked are $\overline{RS}$ and $\overline{AB}$ .

The ratio of $\overline{RS}:\overline{AB}$ is $18:24\implies \boxed{3:4}$ .

The reason why it ideally should be $3:4$ and not $4:3$ is because the question states $RTSU\sim ABCD$ , which mentions $RSTU$ first, so our answer should follow this respective order. I believe you were marked right anyways because the specific order is not specified, but generally, you want to give your answer respectively by default.