Many texts in the mathematical literature use ⊂ to mean ⊆, so it is best to use the proper subset unicode character ⊊.
Apparently some textbook writer is trying to change the meaning of ⊂ to match <, but that horse left the barn 120 years ago.
Question:
Determine whether
Set A equals Set B, A=B,
Set A is a subset of Set B, A ⊆ B,
Set B is a subset of Set A, B ⊆ A,
Set A is a proper subset of Set B, A ⊊ B,
Set B is a proper subset of Set A, B ⊊ A
or if none of these answer applies.
Set A is the set of odd counting numbers smaller than 66.
Set B is the set of odd natural numbers between 0 and 66.
Answer: A = B and A ⊆ B and B ⊆ A.
Step-by-step explanation:
Counting numbers are integers > 0.
Natural numbers are integers >= 0.
"N between x and y" might mean either x <= N <= y or x < N < y, but if N is odd and x and y are even, it doesn't matter.
A = {odd counting numbers < 66}
= {1, 3, 5, ..., 65}
B = {odd natural numbers N with 0 <= N <= 66}
= {1, 3, 5, ..., 65}
The sets are the same.
A = B and A ⊆ B and B ⊆ A.
A ⊊ B is false.
B ⊊ A is false.
