Homework Sourse1 Assume that A and B are sets Let A represent the complemen
1. Assume that A and B are sets. Let !A represent the complement of A. Which of the following choices is an equivalent way to express the set A – ( A – B ) ?
A) A U B B) A B C) A – B D) B – A E) None of the above
2. Assume that A and B are sets. Let !A represent the complement of A. Which of the following choices is an equivalent way to express the set A – ( A B ) ?
A) A U B B) A B C) A – B D) B – A E) None of the above
3. Assume that A and B are sets. Let !A represent the complement of A. Which of the following choices is an equivalent way to express the set ( A U B ) - A ?
A) A U B B) A B C) A – B D) B – A E) None of the above
4. Assume that A and B are sets. Let !A represent the complement of A. Which of the following choices is an equivalent way to express the set ( A – B ) U ( B – A ) U ( A B ) ?
A) A U B B) A B C) A – B D) B – A E) None of the above
5. Assume that A and B are sets. Let !A represent the complement of A. Which of the following choices is an equivalent way to express the set ! ( !A U ! B ) ?
A) A U B B) A B C) A – B D) B – A E) None of the above
6. Assume that A and B are sets. Let !A represent the complement of A. Which of the following choices is an equivalent way to express the set ! ( ! A ! B ) ?
A) A U B B) A B C) A – B D) B – A E) None of the above
Thanks a lot for your help!!!
Solution
Answer1)
B) A B
Example:
a={1,2,3}
b={1,2}
A-(A-B)=>{1,2,3}-{3} =>{1,2}
A B => {1,2}
Answer2)
C) A - B
Example:
a={1,2,3}
b={1,2}
A-(AB)=>{1,2,3}-{1,2} =>{3}
A-B => {3}
Answer3)
D) B-A
Example:
a={1,2,3}
b={1,2,3,4}
(AUB)-A=>{1,2,3,4}-{1,2,3} =>{4}
B-A => {3}
Answer4)
A) A U B
Example:
a={1,2,3}
b={1,2}
(A–B)U(B–A)U(AB)=>{3}U{}U{1,2} =>{1,2,3}
AUB=> {1,2,3}
Answer5)
B) AB
Example:
= {1, 2, 3, 4, 5, }
a={1,2,3}
b={1,2,4}
!(!AU!B)=> ! ( {4,5} U {3,5} ) =>!{3,4,5}=> {1,2}
AB=> {1,2,3}
Answer6)
A) AUB
Example:
= {1, 2, 3, 4, 5, }
a={1,2,3}
b={1,2,4}
!(!A!B)=> ! ( {4,5} {3,5} ) =>!{5}=> {1,2,3,4}
AUB=> {1,2,3}
