# 4.5 Arguments

4.5 Arguments

(A) Premises and Conclusions

1. An argument is a process of making conclusion based on several given statements.
2. The statements given are known as premises.
3. An argument consists of premises and a conclusion.

Example 1:
Identify the premises and conclusion of the following argument.
(a) 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

1. 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 $\cap$ Q = P.
Premise 2P $\cap$ Q $\ne$ P
Conclusion: ______________

Solution:
Conclusion: P is not the subset of Q.