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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1 Answer
Mar 9, 2018

Answer:

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!