Question

Let U​ = {t,u,v,w,x,y,z}, A​ = ​{​}, D​ = ​{​}, C​ = ​{​}, B​ = ​{​}. Tell whether the statement below is true or false. U is the universal set.

A) The set U includes all elements t,u,v,w,x,y,z, representing the universal set.
B) The set U does not include all elements t,u,v,w,x,y,z, and thus, it is not the universal set.
C) The information provided is insufficient to determine if U is the universal set.
D) Some elements are missing from set U, making it only partially representative of the universal set.

Answer 1

The statement that the set U = {t,u,v,w,x,y,z} is the universal set is true, as no additional elements or sets with different elements are provided, making U inclusive of all relevant elements in this context.

Step-by-step explanation:

The question pertains to determining whether a given set, U, is a universal set based on its definition and the elements it includes. In set theory, the universal set is the set that contains all objects or elements, and in the context of a particular discussion or problem, it includes all the elements under consideration. According to the information provided, the set U = {t,u,v,w,x,y,z} is presented as the universal set for this particular context. Since there are no other elements or sets provided that contain elements outside of U, and all other given sets A, B, C, and D are empty, it suggests that U includes all the elements that are relevant to this context. Therefore, the correct statement is:

The set U includes all elements t, u, v, w, x, y, z, representing the universal set.

This is true as no additional elements are mentioned outside the set U, and no counterexamples are provided that belong to the universal set but are not in U.