# IDENTIFYING PARTS OF A LOGIC STATEMENT

## About "Identifying Parts of a Logic Statement"

Identifying Parts of a Logic Statement :

In this section, we will begin by identifying parts of a logic statement.  Once you have mastered that, we will begin to move the parts around and see what happens.

## Identifying Parts of a Logic Statement

Conditional :

Conditional - (p --> q) The given hypothesis and conclusion

Example :

If i finish my math homework, then i will go to the movies.

Hypothesis :

I finish my math homework.

Conclusion :

I will go to the movies.

Converse :

Converse - (q --> p) Exchanging the hypothesis and the conclusion of the conditional.

Example :

Initial conditional statement :

If i finish my math homework, then i will go to the movies.

Converse statement :

If i go to the movies, then i have finished my math homework.

Inverse :

Converse - (∼ p --> ∼ q) Negating both the hypothesis and the conclusion of the conditional.

Example :

Initial conditional statement :

If i finish my math homework, then i will go to the movies.

Inverse statement :

If i do not finish my math homework, then i will not go to the movies.

Contrapositive :

Contrapositive - (q --> ∼ p) Negating both the hypothesis and the conclusion of the converse statement.

Example :

Initial conditional statement :

If i finish my math homework, then i will go to the movies.

Converse statement :

If i go to the movies, then i finished my math homework.

Inverse statement :

If i do not go to the movies, then i did not finish my math homework.

## Identifying Parts of a Logic Statement - Examples

Example 1 :

Write the converse, inverse and contrapositive of the following conditional statement :

If a figure is a square, then it is a rectangle

Given the Conditional Statement :

If a figure is a square, then it is a rectangle

Converse :

If a figure is a rectangle, then it is a square

Inverse :

If a figure is not a square, then it is not a rectangle

Contrapositive :

If a figure is not a rectangle, then it is not a square

Example 2 :

Write the conditional,converse, inverse and contrapositive of the following statement :

If A, then B

Conditional :

If A, then ∼ B

Converse :

If B, then A

Inverse :

If A, then B

Contrapositive :

If B, then ∼ A

Example 3 :

Write the converse statement of the following :

If it is Monday, then i had chicken for lunch

Converse :

If i had chicken for lunch, then it is Monday

Example 4 :

Write the inverse statement of the following :

If I did not have salad for lunch, then it is not Thursday

Converse :

Example 5 :

Write the inverse statement of the following :

If it is not Thursday, then I did not have salad for lunch

Converse :

Example 6 :

What is the inverse statement of  r → s ?

Converse :

r →  s

Example 7 :

What is the converse statement of t → u ?

Converse :

u →  t

Example 8 :

What is the contrapositive statement of ∼ p→ c ?

Converse :

c→ p After having gone through the stuff above, we hope that the students would have understood how to identify the parts of a logic statement.

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