Determine whether

Upper A equals Upper BA=B ,

Upper A is a subset of Upper BA ⊆ B ,

Upper B is a subset of Upper AB ⊆ A ,

Upper A is a proper subset of Upper BA ⊂ B ,

Upper B is a proper subset of Upper AB ⊂ 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.

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.