Question

consider the conditional statement:

if it is monday, then ill go to school.

match each statement to the correct variation of the conditional statement.

• if i dont go to school, then it is not monday.
• if i go to school, then it is monday.
• if it is not monday, then i will not go to school.

a. inverse
b. converse
c. contrapositive

Explanation:

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<reasoning>

Define the symbolic components of the conditional statement

\[

$$\begin{aligned} &p: \text{"It is Monday"} \\ &q: \text{"I'll go to school"} \\ &\text{Original statement } (p ightarrow q): \text{"If it is Monday, then I'll go to school."} \end{aligned}$$

\]

Define the variations of the conditional statement

\[

$$\begin{aligned} &\text{Converse } (q ightarrow p): \text{"If I go to school, then it is Monday."} \\ &\text{Inverse } ( eg p ightarrow eg q): \text{"If it is not Monday, then I will not go to school."} \\ &\text{Contrapositive } ( eg q ightarrow eg p): \text{"If I don't go to school, then it is not Monday."} \end{aligned}$$

\]

Match each given statement to its variation

\[

$$\begin{aligned} &\text{"If I don't go to school, then it is not Monday."} ightarrow \text{c. contrapositive} \\ &\text{"If I go to school, then it is Monday."} ightarrow \text{b. converse} \\ &\text{"If it is not Monday, then I will not go to school."} ightarrow \text{a. inverse} \end{aligned}$$

\]
</reasoning>

<answer>

Statement	Variation
"If I go to school, then it is Monday."	b. converse
"If it is not Monday, then I will not go to school."	a. inverse

</answer>

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Answer:

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<reasoning>

Define the symbolic components of the conditional statement

\[

$$\begin{aligned} &p: \text{"It is Monday"} \\ &q: \text{"I'll go to school"} \\ &\text{Original statement } (p ightarrow q): \text{"If it is Monday, then I'll go to school."} \end{aligned}$$

\]

Define the variations of the conditional statement

\[

$$\begin{aligned} &\text{Converse } (q ightarrow p): \text{"If I go to school, then it is Monday."} \\ &\text{Inverse } ( eg p ightarrow eg q): \text{"If it is not Monday, then I will not go to school."} \\ &\text{Contrapositive } ( eg q ightarrow eg p): \text{"If I don't go to school, then it is not Monday."} \end{aligned}$$

\]

Match each given statement to its variation

\[

$$\begin{aligned} &\text{"If I don't go to school, then it is not Monday."} ightarrow \text{c. contrapositive} \\ &\text{"If I go to school, then it is Monday."} ightarrow \text{b. converse} \\ &\text{"If it is not Monday, then I will not go to school."} ightarrow \text{a. inverse} \end{aligned}$$

\]
</reasoning>

<answer>

Statement	Variation
"If I go to school, then it is Monday."	b. converse
"If it is not Monday, then I will not go to school."	a. inverse

</answer>

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