# 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!

Mar 9, 2018

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

$B = \left\{x : x \le \textcolor{red}{15}\right\}$

and for other answers it is

$B = \left\{x : x \le \textcolor{red}{5}\right\}$

#### 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).

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

A is the subset of $\epsilon$ greater than 5.

$A = \left\{6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17\right\}$

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

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

OR...

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

$B = \left\{1 , 2 , 3 , 4 , 5\right\}$

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

$A \cap B = \emptyset$

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

$A ' = \left\{1 , 2 , 3 , 4 , 5\right\}$

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

$A ' \cap B = \left\{1 , 2 , 3 , 4 , 5\right\}$

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

$A \cap B ' = \left\{16 , 17\right\}$

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.

$\left(A \cap B '\right) ' = \left\{1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15\right\}$

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!