[Mathematic Form 4] Lines of Argument

An argument involves a given set of statements called premises. From the statements, a conclusion can be made.

The following are three simple forms of arguments that can be used to make a conclusion.

Argument (Form I)
Premise 1 : All A are B
Premise 2 : C is A
Conclusion: C is B
Eg:
Premise 1 : All heptagons have 7 sides.
Premise 2 : Object Y is a heptagon.
Conclusion: Object Y has 7 sides

Argument (Form II)
Premise 1 : If p, the q.
Premise 2 : p is true.
Conclusion: q is true
Eg:
Premise 1 : If k = 5, then 3k - 1 = 14
Premise 2 : k = 5
Conclusion: 3k - 1 = 14

Argument (Form III)
Premise 1 : If p, then q.
Premise 2 : Not q is true.
Conclusion: Not p is true.
Eg:
Premise 1 : If an integer, x, is a factor of 6, it is also a factor of 12.
Premise 2 : x is not a factor of 12
Conclusion: x is not a factor of 6

More Arguments...

1. Premise 1 : If x is an even number, it is divisible by 2.
Premise 2 : x is an even number.
Conclusion: x is divisible by 2.

2. Premise 1 : If p > q, then p > r.
Premise 2 : p > q.
Conclusion: p > r.

3. Premise 1 : All hexagons have six sides.
Premise 2 : J is a hexagon.
Conclusion: J has six sides.

4. Premise 1 : If cos x = 0.5, then x = 60^o or 120^o
Premise 2 : cos x = 0.5
Conclusion: x = 60^o or 120^o

5. Premise 1 : All prime numbers have only two factors.
Premise 2 : 9 is not a prime number.
Conclusion: 9 has more than two factors.