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2 years ago

What is the length of the edge of a cube with a wolume of 512?

1 answer:

3 0

A≈8
V Volume

Using the formula
V=a3
Solving fora
a=V⅓=512⅓≈8

Therefore, to find the lenght of an edge of the cube, just find the cube root of the volume. In this case, the cube root of 512 is equal to 8.

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1 year ago

e) Given the following: Let X = {1, 2, 3, 4) and a relation R on X as R= {(1,2), (2,3), (3,4)}. Find the reflexive and transitiv

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Answer:

The answer is $\{(1,1),(2,2),(3,3),(4,4),(1,2)(2,3)(3,4),(1,3),(1,4)\}$

Step-by-step explanation:

Remember that a reflexive relation $R\subset \mathcal{P}(X)$ , where $\mathcal{P}(X)$ is the power set of $X$ , is one which conteins the ordered pairs of the form $(a,a)$ , for $a\in X$ .

So, As the reflexive and transitive closure of $R$ (that we will denote by $\overline{R}$ ) is in particular reflexive, we must add to $R$ the elements $\{(1,1) , (2,2),(3,3),(4,4) \}$

A transitive relation $R$ is one in which if the pair $(a,b)$ and the pair $(b,c)$ are in there, then the pair $(a,c)$ must be there too.

So, to complete the relation $R$ to be reflexive and transitive we must add the pair $(1,3)$ (because $(1,2),(2,3)$ are in $R$ ), the pair $(2,4)$ , and the pair $(1,4)$ because we added the pair $(2,4)$ .

Therfore we have that $\overline{R}=\{(1,1),(2,2),(3,3),(4,4),(1,2)(2,3)(3,4),(1,3),(1,4)\}$ .

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3 years ago

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