An undisclosed number of friends gather for dinner. Each person shakes each other persons hand exactly once. How many handshakes occur?

Question

Piti reasons that 2 people will have one handshake. For each person added, everyone in the earlier group will need to shake the new persons hand. So, when a third person is added there will be two new handshakes and therefore 1+2=3 handshakes altogether. Similarly, when the fourth person is added there will be 1+2+3=6 handshakes and when the fifth person is added there will be 1+2+3+4=10 handshakes. Piti concludes that if n people attend a party, there will be 1+2+3+...+(n-1) handshakes altogether.
A.) Explain how Pitis argument is inductive
B.) Explain how Pitis argument is deductive

Answer 1

deductive:
So, when a third person is added there will be two new handshakes and therefore 1+2=3 handshakes altogether. Similarly, when the fourth person is added there will be 1+2+3=6 handshakes and when the fifth person is added there will be 1+2+3+4=10 handshakes.

Inductive:Piti concludes that if n people attend a party, there will be 1+2+3+...+(n-1) handshakes altogether.