# 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!

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#### Explanation

Explain in detail...

#### Explanation:

I want someone to double check my answer

3
Joe B. Share
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!

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