**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.

**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.

**Example 1 : **

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

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

**Answer : **

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

**Answer : **

**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

**Answer : **

**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

**Answer : **

**Converse : **

If i had salad for lunch, then it is Thursday

**Example 5 : **

Write the inverse statement of the following :

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

**Answer : **

**Converse : **

If i had salad for lunch, then it is Thursday

**Example 6 : **

What is the inverse statement of **∼** r → s ?

**Answer : **

**Converse : **

r → **∼** s

**Example 7 : **

What is the converse statement of **∼ **t → u ?

**Answer : **

**Converse : **

u → **∼** t

**Example 8 : **

What is the contrapositive statement of ∼ p→ c ?

**Answer : **

**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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