Question

construct a venn diagram where ( u = { a, b, c, d, e, f, g } ), ( a = { b, g } ), and ( b = { a, c } ). move each of the lettered points to an appropriate region on the venn diagram. provide your answer below:

Explanation:

Step1: Identify elements in set A only

Elements in \(A=\{b, g\}\) but not in \(B = \{a,c\}\). So \(b\) and \(g\) go in the region of circle \(A\) that does not overlap with circle \(B\).

Step2: Identify elements in set B only

Elements in \(B=\{a,c\}\) but not in \(A=\{b,g\}\). So \(a\) and \(c\) go in the region of circle \(B\) that does not overlap with circle \(A\).

Step3: Identify elements in neither A nor B

Elements \(d\), \(e\), \(f\) are in the universal set \(U=\{a,b,c,d,e,f,g\}\) but not in \(A\) or \(B\). So \(d\), \(e\), \(f\) go in the region of the rectangle (universal set) outside both circles \(A\) and \(B\).

Answer:

• \(a\) and \(c\) are in the non - overlapping part of circle \(B\).
• \(b\) and \(g\) are in the non - overlapping part of circle \(A\).
• \(d\), \(e\), \(f\) are in the region of the universal set outside both circles \(A\) and \(B\).