At Westonci.ca, we provide reliable answers to your questions from a community of experts. Start exploring today! Discover solutions to your questions from experienced professionals across multiple fields on our comprehensive Q&A platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
To determine which of the given true conditional statements has a true converse, let's first recall the definition of a converse. The converse of a conditional statement "If [tex]\( P \)[/tex], then [tex]\( Q \)[/tex]" is "If [tex]\( Q \)[/tex], then [tex]\( P \)[/tex]".
We will analyze each of the given true conditional statements and their converses.
1. Statement: If [tex]\( x > 3 \)[/tex], then [tex]\( x > 2 \)[/tex].
- Converse: If [tex]\( x > 2 \)[/tex], then [tex]\( x > 3 \)[/tex].
This converse is not always true because there are values of [tex]\( x \)[/tex] (for example, [tex]\( x = 2.5 \)[/tex]) that are greater than 2 but not greater than 3. Therefore, this converse is false.
2. Statement: If [tex]\( x > 3 \)[/tex], then [tex]\( 2x > 6 \)[/tex].
- Converse: If [tex]\( 2x > 6 \)[/tex], then [tex]\( x > 3 \)[/tex].
To check if this converse is true, we can solve the inequality [tex]\( 2x > 6 \)[/tex]. Dividing both sides by 2, we get [tex]\( x > 3 \)[/tex]. This is exactly the same as the original condition. Therefore, this converse is true.
3. Statement: If [tex]\( x > 3 \)[/tex], then [tex]\( x > -3 \)[/tex].
- Converse: If [tex]\( x > -3 \)[/tex], then [tex]\( x > 3 \)[/tex].
This converse is false because there are many values of [tex]\( x \)[/tex] (for example, [tex]\( x = 0 \)[/tex]) that are greater than -3 but not greater than 3.
4. Statement: If [tex]\( x > 3 \)[/tex], then [tex]\( x > 0 \)[/tex].
- Converse: If [tex]\( x > 0 \)[/tex], then [tex]\( x > 3 \)[/tex].
This converse is also false because there are values of [tex]\( x \)[/tex] (for example, [tex]\( x = 1 \)[/tex]) that are greater than 0 but not greater than 3.
Based on this analysis, the true conditional statement that has a true converse is the second statement:
If [tex]\( x > 3 \)[/tex], then [tex]\( 2x > 6 \)[/tex].
Thus, the correct answer is the second statement.
We will analyze each of the given true conditional statements and their converses.
1. Statement: If [tex]\( x > 3 \)[/tex], then [tex]\( x > 2 \)[/tex].
- Converse: If [tex]\( x > 2 \)[/tex], then [tex]\( x > 3 \)[/tex].
This converse is not always true because there are values of [tex]\( x \)[/tex] (for example, [tex]\( x = 2.5 \)[/tex]) that are greater than 2 but not greater than 3. Therefore, this converse is false.
2. Statement: If [tex]\( x > 3 \)[/tex], then [tex]\( 2x > 6 \)[/tex].
- Converse: If [tex]\( 2x > 6 \)[/tex], then [tex]\( x > 3 \)[/tex].
To check if this converse is true, we can solve the inequality [tex]\( 2x > 6 \)[/tex]. Dividing both sides by 2, we get [tex]\( x > 3 \)[/tex]. This is exactly the same as the original condition. Therefore, this converse is true.
3. Statement: If [tex]\( x > 3 \)[/tex], then [tex]\( x > -3 \)[/tex].
- Converse: If [tex]\( x > -3 \)[/tex], then [tex]\( x > 3 \)[/tex].
This converse is false because there are many values of [tex]\( x \)[/tex] (for example, [tex]\( x = 0 \)[/tex]) that are greater than -3 but not greater than 3.
4. Statement: If [tex]\( x > 3 \)[/tex], then [tex]\( x > 0 \)[/tex].
- Converse: If [tex]\( x > 0 \)[/tex], then [tex]\( x > 3 \)[/tex].
This converse is also false because there are values of [tex]\( x \)[/tex] (for example, [tex]\( x = 1 \)[/tex]) that are greater than 0 but not greater than 3.
Based on this analysis, the true conditional statement that has a true converse is the second statement:
If [tex]\( x > 3 \)[/tex], then [tex]\( 2x > 6 \)[/tex].
Thus, the correct answer is the second statement.
We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.
