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

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

These are the two questions I need help with. Thanks in advance.

A.) Piti's argument is inductive because it starts with specific observations and examples (such as adding one person at a time and noting the number of handshakes) and then generalizes to a broader conclusion about the total number of handshakes when n people attend a party. The pattern observed is that each additional person leads to a certain number of new handshakes, which is determined by adding the number of handshakes of the previous group to the number of people in the new group. This generalization is inferred from the specific examples and observations and is applied to any number of people in attendance at the party.

B.) Piti's argument can also be seen as deductive because it follows a logical pattern using mathematical principles. The deduction starts with the premise that whenever n people attend a party, there will be 1+2+3+...+(n-1) handshakes altogether. This is based on the observation of adding one person at a time and noting the number of handshakes. From this premise, Piti deduces that the total number of handshakes can be calculated by summing the sequence of consecutive numbers from 1 to (n-1). The deduction relies on the logical inference that the number of handshakes follows a specific pattern based on the number of people present.