__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: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

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:Solution:

**Conclusion**: 45 is divisible by 5.

Argument Form II

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:Solution:

**Conclusion**: 3 is a factor of 54.

Argument Form III

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 2**:

*P*$\cap $

*Q*$\ne $

*P*

**Conclusion**: ______________

Solution:Solution:

**Conclusion**:

*P*is not the subset of

*Q*.