John and Mary do not know each other, and have never met. However, they discover each other on a dating app, and decide to meet up. It turns out that John has Covid-19, but has not been tested. Mary is free of disease. Consider the following events: A= {The date goes ahead, regardless of John's disease.}, B= {John infects Mary with the virus.}, C= {Mary comes down with Covid-19.}, D= {John gets tested before the date and finds he is positive.}, E= {Mary gets tested after the date and finds she is positive.} (a) Write a Boolean expression to represent the event: John meets Mary and Mary gets Covid-19 but does not get it from John.. (b) Construct a Venn diagram of A, B, and C. On the diagram i. Shade in the regions that are impossible (using common sense.) ii. Outline the region that represents the event in 3a (c) Using Boolean algebra or Venn or Euler diagrams, demonstrate that ( (DcA) (DAc) ) BC= ABCDc. (You many need to use the answer to 3(b)i to confirm this.) Describe this event in English, using a complete sentence.