Question

eight students form a math homework group. the students in the group are joe, earl, zippy, annette, stinky, muriel, chet, and oswaldo. prior to forming the group, stinky was friends with everyone but muriel. muriel was friends with zippy, annette, chet, and earl. joe was friends with stinky, earl, oswaldo, and zippy. letting an edge between two students represent friendship, which of the following graphs models the friendships among these students? which of the graphs models the the friendships? \bigcirc graph i \bigcirc graph ii

Explanation:

Step1: Analyze Joe's friendships

Joe was friends with Stinky, Earl, Oswaldo, and Zippy. So there should be edges between Joe (J) - Stinky (S), Joe (J) - Earl (E), Joe (J) - Oswaldo (O), Joe (J) - Zippy (Z).

Step2: Analyze Muriel's friendships

Muriel (M) was friends with Zippy (Z), Annette (A), Chet (C). So there should be edges between Muriel (M) - Zippy (Z), Muriel (M) - Annette (A), Muriel (M) - Chet (C).

Step3: Analyze Stinky's friendships

Stinky was friends with everyone but Muriel. So there should be edges from Stinky (S) to Joe (J), Zippy (Z), Annette (A), Earl (E), Oswaldo (O), Chet (C).

Step4: Check the graphs

In Graph I, the edges match the friendship relations:

• For Joe: there are edges to S, E, O, Z.
• For Muriel: there are edges to Z, A, C.
• For Stinky: there are edges to J, Z, A, E, O, C (excluding M as per the condition).

In Graph II, the connections do not fully match the described friendships (for example, the connections from Stinky may be incomplete when compared to the friendship list).

Answer:

Graph I