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.

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.

(a) the volume of the cone is 20/3 in3

hence, option a is correct.