The following Venn diagram shows three sets A (red), B (blue), and C (green) con
ID: 3846863 • Letter: T
Question
The following Venn diagram shows three sets A (red), B (blue), and C (green) contained within a universe set named U (violet). In the diagram, different subsets (regions) are labeled by the numbers 1 through 8. Thus, set A contains subsets labeled 1, 2, 4, and 5; set B contains subsets labeled 2, 3, 5, and 6; set C contains subsets labeled 4, 5, 6, and 7; set U contains subsets labeled 1 through 8 (i.e., the universe). Now, give the labels (i.e., numbers) of all the subsets that are contained in each of the following sets:
(a) (¬A) B.
(b) A–(B C).
(c) {x| x A or x B}.
(d) {x| x A and x (B C)}.
(e) (A B) (¬C).
B 3 6 C 47 8Explanation / Answer
(a) (¬A) B
= {3,6,7,8} {2,3,5,6} = {3,6}
(b) A–(B C)
= {1,2,4,5} - (2,3,4,5,6,7}
= 1
(c) {x| x A or x B}.
= {1,2,4,5,7,8}
(d) {x| x A and x (B C)}.
= 1,2,4
(e) (A B) (¬C).
= {1,2,3,4,5,6} {1,2,3,8}
= {1,2,3,4,5,6,8}