## Problem-82

**Problem-82**

The** intersection graph** of a collection of sets *A*1, *A*2, . . . , *An* is the graph that has a vertex for each of these sets and has an edge connecting the vertices representing two sets if these sets have a nonempty intersection. Select the** **intersection graph of these collections of sets.

**a)**

A1={0, 2, 4, 6, 8}, A2={0, 1, 2, 3, 4},

A3={1, 3, 5, 7, 9}, A4={0, 1, 8, 9},

A5={5, 6, 7, 8, 9}.

**b)**

A1={. . . ,−6,−3, 0, 3, 6, . . .}, A2={. . . ,−4,−3,−2,−1, 0},

A3={. . . ,−2,−1, 0, 1, 2, . . .}, A4={. . . ,−6,−4,−2, 0, 2, 4, 6, . . .},

A5={. . . ,−5,−3,−1, 1, 3, 5, . . .}.

**c)**

A1={x|0<x<1}, A2={x|−1<x<1},

A3={x|x>−1}, A4=R,

A5={x|x<0}, A6={x|−1<x<0}.

**Solution**

**a)**

**b)**

**c)**

I was wondering if you knew where to find a program, hopefully free, that would allow me to construct graphs out of directions like this problem has. Thanks