A, B and C are subsets of the universal set U such that : \(U = {0, 1, 2, 3,..., 12}; A = {x : 0 \leq x \leq 7}; B = {4, 6, 8, 10, 12}; C = {1 < y < 8}\), w...
Question 1 Report
A, B and C are subsets of the universal set U such that : \(U = {0, 1, 2, 3,..., 12}; A = {x : 0 \leq x \leq 7}; B = {4, 6, 8, 10, 12}; C = {1 < y < 8}\), where y is a prime number.
(a) Draw a venn diagram to illustrate the information given above;
(b) Find: (i) \((B \cup C)'\); (ii) \(A' \cap B \cap C\).
Answer Details
(a) Venn diagram
First, write the sets in roster form:
\[A=\{0,1,2,3,4,5,6,7\},\quad B=\{4,6,8,10,12\},\quad C=\{2,3,5,7\}.\]
(b)(i)
\[B\cup C=\{2,3,4,5,6,7,8,10,12\}.\]
Therefore, relative to \(U=\{0,1,2,\ldots,12\}\),
\[(B\cup C)'=\{0,1,9,11\}.\]
(b)(ii)
\[A'=\{8,9,10,11,12\}.\]
Since \(B\cap C=\varnothing\),
\[A'\cap B\cap C=\varnothing.\]
Download The App On Google Playstore
Everything you need to excel in your exams
