Question

Here X=R. τ={∅,R,(−[infinity],9],[1,[infinity]),[1,9]} Here you can not enter letters, your answer must be an interval or union of intervals.

R =

Answer 1

The question involves set theory in mathematics, where the set τ contains distinct intervals on the real number line. Square brackets denote inclusive boundaries and parentheses indicate exclusive ones.

Step-by-step explanation:

The student's question appears to deal with set theory and intervals on the real number line. Specifically, it mentions the set τ, which includes the empty set, the entire set of real numbers, and various intervals. The main goal is to understand how sequences of intervals and union of intervals function in set theory and to be able to express these sets using interval notation.

To define the intervals given in the question, first, we need to understand the brackets used: the square bracket '[' indicates that the boundary is included in the interval, whereas the parenthesis '(' indicates that the boundary is not included. Therefore, the set τ from the question consists of the following intervals on the real number line:

The empty set, denoted by ∅.

The entire set of real numbers, denoted by ℝ.

The interval from negative infinity up to and including 9, denoted as (-∞, 9].

The interval from 1 to infinity, denoted as [1, ∞).

The interval from 1 to 9, inclusive of both ends, denoted as [1, 9].