For each $n \in \mathbb{n}$, let $a_n = [n] \times [n]$. define $b = \bigcup_{n \in \mathbb{n}} a_n$. does $b = \mathbb{n} \times \mathbb{n}$? either prove that it does, or show why it does not.

No, it is not.

Step-by-step explanation:

The set contains every ordered pair of Natural numbers, while B only contains those pairs in which both values in each entry are the same. Therefore, C is a bigger set than B, but B is not equal to C because for example C contains and B doesnt because 1 is not equal to 2.

-4

step-by-step explanation:

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.