Apeejay Stya University, Sohna, Gurgaon Course Code: ETCS-102 Subject: Discrete Mathematical structures Faculty Name: Vikas Jindal Time Required: 05 hrs Due Date: Nov 02, 2015 Max Marks: 5 ________________________________________________________________________ Assignment - 1 Problem #1 When n couples arrived at a party, they were greeted by the host and the hostess at the door. After rounds of handshaking, the host asked the guests and his wife (the hostess) to indicate the number of hands each of them had shaken. He got 2n+1 different answers. Given that no one shook hands with his or her spouse, how many hands had the hostess shaken? Prove your result by induction. Problem #2 Write the following statements in symbolic form: i) The sun is bright and the humidity is not high. ii) If I finish my homework before dinner and it does not rain, then I will go to the ball game. iii) If you do not see me tomorrow, it means I have gone to Chicago. iv) If the utility cost goes up or the request for additional funding is denied, then a new computer will be purchased if and only if we can show that the current computing facilities are indeed not adequate. Problem #3 A certain country is inhabited only by people who either always tell the truth or always tell lies, and who will respond to the questions only with a \"yes\" or \"no.\" A tourist comes to a fork in the road, where one branch leads to the capital and the other does not. There is not sign indicating which branch to take, but there is an inhabitant, Mr Z standing at the fork. What single question should the tourist ask him to determine which branch to take