Question

for the given sets, construct a venn diagram and place the elements in the proper region. let ( u = { c, d, g, h, k, u, q } ) ( a = { d, h, g, q } ) ( b = { c, d, h, u } )

Explanation:

Step1: Find the intersection of A and B

The intersection \(A\cap B\) is the set of elements that are in both \(A\) and \(B\).
\(A = \{d,h,g,q\}\), \(B=\{c,d,h,u\}\)
\(A\cap B=\{d,h\}\)

Step2: Find elements only in A

Elements only in \(A\) are \(A - (A\cap B)=\{g,q\}\)

Step3: Find elements only in B

Elements only in \(B\) are \(B-(A\cap B)=\{c,u\}\)

Step4: Find elements in the universal set but not in A or B

\(U=\{c,d,g,h,k,u,q\}\), \(A\cup B = \{c,d,h,g,q,u\}\)
\(U-(A\cup B)=\{k\}\)

Answer:

The third Venn - diagram in the list (the one with \(k\) outside the circles, \(g,q\) only in \(A\), \(c,u\) only in \(B\) and \(d,h\) in the intersection) is the correct one.