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
A.) Piti's argument is inductive because he starts with a specific observation (two people shaking hands) and then generalizes it to a larger group by using patterns and making a generalized statement. By observing the pattern and applying it to increasing numbers of people, he concludes that the total number of handshakes can be calculated by the formula 1+2+3+...+(n-1).
B.) Piti's argument is deductive because he uses logical reasoning based on a given rule or principle to reach a specific conclusion. He starts with the premise that each person shakes each other person's hand exactly once and uses this information to deduce the formula for calculating the total number of handshakes. He does not rely on specific observations or patterns, but instead uses logical deduction based on the given rule.
A.) Piti's argument is inductive because it involves reasoning from specific cases to a general conclusion. Piti observes the pattern of handshakes as more people are added to the dinner gathering. Based on the specific cases of adding the third, fourth, and fifth person, Piti makes a general claim about the number of handshakes for any number of people attending a party. Piti concludes that if there are n people, there will be 1 + 2 + 3 + ... + (n-1) handshakes altogether. This is an inductive reasoning because it relies on patterns observed in specific cases to make a general statement.
B.) Piti's argument can also be considered deductive because it involves reasoning from a general rule to specific instances. Piti uses the general rule that "each person shakes each other person's hand exactly once" to deduce the number of handshakes for different numbers of people attending the party. By applying this rule systematically, Piti calculates the number of handshakes by summing up the handshakes between each person. Therefore, Piti's argument is deductive because it starts with a general principle and applies it to specific scenarios to derive conclusions.
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.