(A) Premises and Conclusions
- An argument is a process of making conclusion based on several given statements.
- The statements given are known as premises.
- An argument consists of premises and a conclusion.
Example 1:
Identify the premises and conclusion of the following argument.
- A pentagon has 5 sides. ABCDE is a pentagon. Therefore, ABCDE has 5 sides.
Solution:
Premise 1: A pentagon has 5 sides.
Premise 2: ABCDE is a pentagon.
Conclusion: ABCDE has 5 sides.
(B) Forms of Arguments
- Based on two given premises, a conclusion can be made for three different forms of arguments.
Argument Form I
|
Premise 1: All A are B. Premise 2: C is A. Conclusion: C is B. |
Example 2:
Make a conclusion based on the two premises given below.
Premise 1: All multiples of 5 are divisible by 5.
Premise 2: 45 is a multiple of 5.
Conclusion: _______________
Solution:
Conclusion: 45 is divisible by 5.
Argument Form II
|
Premise 1: If p, then q. Premise 2: p is true. Conclusion: q is true. |
Example 3:
Make a conclusion based on the two premises given below.
Premise 1: If a number is a factor of 18, then the number is a factor of 54.
Premise 2: 3 is a factor of 18.
Conclusion: _______________
Solution:
Conclusion: 3 is a factor of 54.
Argument Form III
|
Premise 1: If p, then q. Premise 2: Not q is true. Conclusion: Not p is true. |
Example 4:
Make a conclusion based on the two premises given below.
Premise 1: If P is a subset of Q, then P ∩ Q = P .
Premise 2: P ∩ Q ≠ P
Conclusion: _______________
Solution:
Conclusion: P is not the subset of Q.