Question

Looking for answers for a)iv), a)v) and c)... Is my brain not working or are the answers in my book wrong? An explained answer is much appreciated!

Answer 1

Answers in your book are inconsistent in their definition of set B! The definition for some answers is

`B ={x: x<= color(red)(15)}`

and for other answers it is

`B ={x: x<= color(red)(5)}`

Explanation:

y is in the set of integers between 1 and 17, inclusive (0 is not considered positive and y is strictly less than 18).

`epsilon = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17}`

A is the subset of `epsilon` greater than 5.

`A = {6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17}`

B is the subset of `epsilon` less than or equal to 15.

`B = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}`

OR...

B is the subset of `epsilon` less than or equal to 5.

`B = {1, 2, 3, 4, 5}`

4 (a) (i) The insection of A and B (the elements that they have in common) is empty.

`A nn B = O/`

4 (a) (ii) The subset "Not A" contains all of the elements in `epsilon` that are NOT in A.

`A' = {1, 2, 3, 4, 5}`

4 (a) (iii) The intersection of "Not A" and B contains all of the elements that these subsets have in common.

`A' nn B = {1, 2, 3, 4, 5}`

4 (a) (iv) The intersection of A and "Not B" contains all of the elements that these subsets have in common.

`A nn B' = {16, 17}`

4 (a) (v) The complement of the intersection of A and "Not B" contains all of the elements EXCEPT those that these subsets have in common.

`(A nn B')' = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}`

4 (b) The union of A and B combines the contents of the two subsets, which equals the contents of `epsilon`.

4 (c) The book's answer makes NO sense!