Question

a city is planning a multicultural festival. a group will perform a chinese fan dance on the main
stage. there are 7 time slots available for the main stage. one group can perform during each of
the time slots listed below.
saturday: 5:00 pm, 6:00 pm, 7:00 pm, 8:00 pm
sunday: 4:00 pm, 5:00 pm, 6:00 pm

• event r is a time slot on saturday.
• event s is a time slot of 6:00 pm or earlier.
• event t is a time slot of 7:00 pm or later.

which event is a subset of another event?

Explanation:

Step1: Define each event's time slots

• Event R (Saturday time slots): {5:00 PM, 6:00 PM, 7:00 PM, 8:00 PM}
• Event S (6:00 PM or earlier): Saturday: 5:00 PM, 6:00 PM; Sunday: 4:00 PM, 5:00 PM, 6:00 PM → {4:00 PM, 5:00 PM, 6:00 PM, 5:00 PM, 6:00 PM} (remove duplicates: {4:00 PM, 5:00 PM, 6:00 PM})
• Event T (7:00 PM or later): Saturday: 7:00 PM, 8:00 PM; Sunday: none → {7:00 PM, 8:00 PM}

Step2: Check subset relationships

• Check T vs R: All elements of T ({7:00 PM, 8:00 PM}) are in R ({5:00 PM, 6:00 PM, 7:00 PM, 8:00 PM}). So T is a subset of R.
• Check S vs R: S has 4:00 PM, 5:00 PM, 6:00 PM. 4:00 PM is not in R (R is only Saturday), so S is not a subset of R.
• Check S vs T: S has times ≤6:00 PM, T has ≥7:00 PM. No overlap, so no subset.

Answer:

Event T is a subset of Event R.