FINITE MATH HELP

Question

(a)    A^c ∩ (B ∩ C ^c)

 

Let U = {7, 8, 9, 10, 11, 12, 13, 14, 15, 16}, A = {7, 9, 11, 13, 15}, B = {8, 10, 12, 14, 16}, and C = {7, 8, 10, 11, 14, 15}. List the elements of each set. (Enter your answers using roster notation. Enter EMPTY or ∅ for the empty set.)

(b)    (A ∪ B^c) ∪ (B ∩ C^c)

 

(c)    (A ∪ B)^c ∩ C ^c

 

Answer 1

complement of the set notation and denoted with ~ (the tilde)

intersection of the set notation and denoted with & (the ampersand)

union of the set set notation and denoted with u

ex. ~X is the complement of X; elements not in X

~B = {7,9,11,13,15}

~C = {9,12,13,16}

A u B = U

(A u ~B) = A=~B , what a coincidence!

B & ~C = {12,16}

so part B is {7,9,11,12,13,15,16}

part c goes like this...

Since A u B is the universal set,

~(A u B) is the empty set...

anything intersected with the empty set

is the empty set