Question

Joshua enjoys exercising. He observed that he sleeps better when he exercises at night. Compose an if-then statement based on Joshua's observation. Conditional Statement: Inverse Statement: Converse Statement: Contrapositive Statement:

Answer 1

Based on Joshua's observation, we can create the following if-then statement:

If Joshua exercises at night, then he sleeps better.

Let's break down the different parts of this statement:

1. If-then statement: This is a type of conditional statement that consists of two parts, the "if" part (the condition) and the "then" part (the result or consequence). In this case, the condition is Joshua exercising at night, and the result is him sleeping better.

2. Inverse statement: The inverse of a conditional statement is formed by negating both the condition and the result. In this case, the inverse statement would be:

If Joshua does not exercise at night, then he does not sleep better.

3. Converse statement: The converse of a conditional statement is formed by swapping the condition and the result. In this case, the converse statement would be:

If Joshua sleeps better, then he exercises at night.

4. Contrapositive statement: The contrapositive of a conditional statement is formed by negating both the swapped condition and the swapped result. In this case, the contrapositive statement would be:

If Joshua does not sleep better, then he does not exercise at night.

It's important to note that while the original conditional statement is true based on Joshua's observation, the inverse, converse, and contrapositive statements may not necessarily be true. The truth value of these statements depends on additional information or evidence.

Answer 2

The if-then statement based on Joshua's observation is: If Joshua exercises at night, then he sleeps better. The inverse statement is: If Joshua does not exercise at night, then he does not sleep better.

Step-by-step explanation:

To write the if-then statement based on Joshua's observation, we need to identify the cause-and-effect relationship. Joshua observed that he sleeps better when he exercises at night. This means that exercising at night is the cause (if) and sleeping better is the effect (then).

So, the if-then statement based on Joshua's observation would be: If Joshua exercises at night, then he sleeps better.

The inverse statement is formed by negating the original statement. So, the inverse of the if-then statement would be: If Joshua does not exercise at night, then he does not sleep better.

The converse statement is formed by reversing the original statement. So, the converse of the if-then statement would be: If Joshua sleeps better, then he exercises at night.

The contrapositive statement is formed by both negating and reversing the original statement. So, the contrapositive of the if-then statement would be: If Joshua does not sleep better, then he does not exercise at night.