Answer :
To identify the inverse of given conditional statements, we need to follow these steps:
1. Write down the original statement.
2. Identify the hypothesis (the "if" part) and the conclusion (the "then" part) of the statement.
3. Create the inverse by negating both the hypothesis and the conclusion of the original statement.
Let's walk through each of the given statements one by one:
### Statement 1:
Original Statement:
"If two points are on the same line, then they are collinear."
Hypothesis: Two points are on the same line.
Conclusion: They are collinear.
Inverse Statement:
To form the inverse, negate both the hypothesis and the conclusion:
"If two points are not on the same line, then they are not collinear."
### Statement 2:
Original Statement:
"Two points are on the same line if and only if they are collinear."
Inverse Statement:
This is a biconditional statement, meaning we have two implications here:
- "If two points are on the same line, then they are collinear."
- "If two points are collinear, then they are on the same line."
For the first part, the inverse is:
"If two points are not on the same line, then they are not collinear."
For the second part, the inverse is:
"If two points are not collinear, then they are not on the same line."
So the inverse statement will be:
"Two points are not on the same line if and only if they are not collinear."
### Statement 3:
Original Statement:
"If two points are collinear, then they are not on the same line."
Hypothesis: Two points are collinear.
Conclusion: They are not on the same line.
Inverse Statement:
To form the inverse, negate both the hypothesis and the conclusion:
"If two points are not collinear, then they are on the same line."
### Statement 4:
Original Statement:
"If two points are not collinear then they are not on the same line."
Hypothesis: Two points are not collinear.
Conclusion: They are not on the same line.
Inverse Statement:
To form the inverse, negate both the hypothesis and the conclusion:
"If two points are collinear, then they are on the same line."
### Statement 5:
Original Statement:
"If two points are not on the same line, then they are not collinear."
Hypothesis: Two points are not on the same line.
Conclusion: They are not collinear.
Inverse Statement:
To form the inverse, negate both the hypothesis and the conclusion:
"If two points are on the same line, then they are collinear."
### Summary:
Here are the original statements along with their inverses:
1. Original: "If two points are on the same line, then they are collinear."
Inverse: "If two points are not on the same line, then they are not collinear."
2. Original: "Two points are on the same line if and only if they are collinear."
Inverse: "Two points are not on the same line if and only if they are not collinear."
3. Original: "If two points are collinear, then they are not on the same line."
Inverse: "If two points are not collinear, then they are on the same line."
4. Original: "If two points are not collinear then they are not on the same line."
Inverse: "If two points are collinear, then they are on the same line."
5. Original: "If two points are not on the same line, then they are not collinear."
Inverse: "If two points are on the same line, then they are collinear."
I hope this clear explanation helps you understand how to find the inverse of conditional statements!
1. Write down the original statement.
2. Identify the hypothesis (the "if" part) and the conclusion (the "then" part) of the statement.
3. Create the inverse by negating both the hypothesis and the conclusion of the original statement.
Let's walk through each of the given statements one by one:
### Statement 1:
Original Statement:
"If two points are on the same line, then they are collinear."
Hypothesis: Two points are on the same line.
Conclusion: They are collinear.
Inverse Statement:
To form the inverse, negate both the hypothesis and the conclusion:
"If two points are not on the same line, then they are not collinear."
### Statement 2:
Original Statement:
"Two points are on the same line if and only if they are collinear."
Inverse Statement:
This is a biconditional statement, meaning we have two implications here:
- "If two points are on the same line, then they are collinear."
- "If two points are collinear, then they are on the same line."
For the first part, the inverse is:
"If two points are not on the same line, then they are not collinear."
For the second part, the inverse is:
"If two points are not collinear, then they are not on the same line."
So the inverse statement will be:
"Two points are not on the same line if and only if they are not collinear."
### Statement 3:
Original Statement:
"If two points are collinear, then they are not on the same line."
Hypothesis: Two points are collinear.
Conclusion: They are not on the same line.
Inverse Statement:
To form the inverse, negate both the hypothesis and the conclusion:
"If two points are not collinear, then they are on the same line."
### Statement 4:
Original Statement:
"If two points are not collinear then they are not on the same line."
Hypothesis: Two points are not collinear.
Conclusion: They are not on the same line.
Inverse Statement:
To form the inverse, negate both the hypothesis and the conclusion:
"If two points are collinear, then they are on the same line."
### Statement 5:
Original Statement:
"If two points are not on the same line, then they are not collinear."
Hypothesis: Two points are not on the same line.
Conclusion: They are not collinear.
Inverse Statement:
To form the inverse, negate both the hypothesis and the conclusion:
"If two points are on the same line, then they are collinear."
### Summary:
Here are the original statements along with their inverses:
1. Original: "If two points are on the same line, then they are collinear."
Inverse: "If two points are not on the same line, then they are not collinear."
2. Original: "Two points are on the same line if and only if they are collinear."
Inverse: "Two points are not on the same line if and only if they are not collinear."
3. Original: "If two points are collinear, then they are not on the same line."
Inverse: "If two points are not collinear, then they are on the same line."
4. Original: "If two points are not collinear then they are not on the same line."
Inverse: "If two points are collinear, then they are on the same line."
5. Original: "If two points are not on the same line, then they are not collinear."
Inverse: "If two points are on the same line, then they are collinear."
I hope this clear explanation helps you understand how to find the inverse of conditional statements!
