Question

Determine if the conclusion that follows from the given statements below is valid. If valid which law was used?
1. if a number is a natural number then it is a whole number
2. if a number is a whole number then it is an integer
Conclusion : if a number is a natural number then it is an integer

Answer 1

Answer:

the conclusion is not valid

Answer 2

Answer: The conclusion is valid by the law of syllogism

The law of syllogism follows the basic form:

If P, then Q

If Q, then R

Therefore, if P then R

We can write it like this

$P \to Q \\\\Q \to R\\\\\therefore P \to R$

We can think of it like starting at town P, moving to Q, then to R. Or we could go from P directly to R if we aren't worried about the town in the middle (town Q).