Answer to Question #338194 in Discrete Mathematics for Agg

Question

U={1,2,3,4,5,6,7,8,9,10}

A={2,3,4,5,8}

B={2,4,6,8,10}

C={1,3,5,7,9}

Instruction: Solve the given below using the sets above

1.( (C U A)-B)’ ∩ (B’ U A)

2.(((BUA)’ U (CUA)’) U ((A-B)’ ∩ (B-C)’))

Answer 1

$2.(BUA)=\{2,3,4,5,6,8,10\}\\(BUA)'=\{1,7,9\}$

$(CUA)=\{1,2,3,4,5,7,8,9\}\\(CUA)'=\{6,10\}$

$((BUA)’ U (CUA)’)=\{1,6,7,9,10\}$

$A-B=\{3,5\}$

$(A-B)'=\{1,2,4,6,7,8,9,10\}$

$B-C=\{2,4,6,8,10\}$

$(B-C)'=\{1,3,5,7,9\}$

$(A-B)' \cap(B-C)'=\{1,7,9\}$

$(((BUA)’ U (CUA)’) U ((A-B)’ ∩ (B-C)’))=\{1,6,7,9,10\}$

1. $(CUA)=\{1,2,3,4,5,7,8,9\}$

$(CUA)-B=\{1,3,5,7,9\}$

$((CUA)-B)'=\{2,4,6,8,10\}$

$B'=\{1,3,5,7,9\}$

$B' U A=\{1,2,3,4,5,7,8,9\}$

$( (C U A)-B)’ ∩ (B’ U A)=\{2,4,8\}$