Question

True or False: [3,4)⊆(3,4)? Explain. a) Define and explain the notation [3,4) and (3,4) in the context of mathematical sets.

b) Instruct the respondent to determine whether the statement is true or false based on the given sets.
c) Encourage a brief explanation or justification for the chosen answer, demonstrating an understanding of set inclusion and interval notation.
Ensure clarity in the question to prompt an accurate assessment and explanation of the statement regarding set inclusion."

Answer 1

The notation [3,4) represents a closed interval and (3,4) represents an open interval. [3,4) is a subset of (3,4), making the statement true.

Step-by-step explanation:

The notation [3,4) represents a closed interval, which means it includes the numbers 3 and 4. The notation (3,4) represents an open interval, which means it includes all numbers between 3 and 4, but not including 3 and 4 themselves.

Based on the given sets, [3,4) is a subset of (3,4). This is because all the numbers in [3,4) are also in (3,4). Therefore, the statement is true.

Set inclusion means that every element in one set is also an element in another set. In this case, every element in [3,4) is also in (3,4), so [3,4) is a subset of (3,4).