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Question 24 Using everyday knowledge, which of the following statements is a conditional statement whose converse is also true? (A) If the TV is unplugged, then the TV will not turn on. (B) If the wind is blowing, then the weather is chilly. C) If an ambulance has emergency lights on, then cars on the road pull over. (D) If the light bulb was recently on, then the light bulb is hot.

Ask by Cummings Gough. in the United States
Jan 24,2025

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Answer

None of the statements have a converse that is also true.

Solution

To determine which of the statements is a conditional statement whose converse is also true, we need to analyze each option. 1. **Understanding Conditional Statements and Their Converses:** - A conditional statement is of the form "If P, then Q" (P → Q). - The converse of this statement is "If Q, then P" (Q → P). 2. **Analyzing Each Statement:** - **(A)** If the TV is unplugged, then the TV will not turn on. - Converse: If the TV will not turn on, then the TV is unplugged. (This is not necessarily true; the TV could be broken or have other issues.) - **(B)** If the wind is blowing, then the weather is chilly. - Converse: If the weather is chilly, then the wind is blowing. (This is not necessarily true; it could be chilly without wind.) - **(C)** If an ambulance has emergency lights on, then cars on the road pull over. - Converse: If cars on the road pull over, then an ambulance has emergency lights on. (This is not necessarily true; cars may pull over for other reasons.) - **(D)** If the light bulb was recently on, then the light bulb is hot. - Converse: If the light bulb is hot, then the light bulb was recently on. (This is also not necessarily true; the bulb could be hot for other reasons.) 3. **Conclusion:** None of the statements provided have a converse that is also true. However, if we consider the nature of the statements, (D) is the closest because a hot light bulb is often a result of being on recently, but it does not guarantee that it was on recently, as it could be hot for other reasons. Thus, the answer is that none of the statements meet the criteria of having a true converse.

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The best example of a conditional statement whose converse is also true is (D) If the light bulb was recently on, then the light bulb is hot. This is because if the light bulb is hot, it can be inferred that it was indeed recently on. Hot bulbs don't just chill out without a reason! On the other hand, conditional statements are everywhere in our lives. Even the simplest situations can be turned into if-then statements! For example, "If it rains, then I’ll take my umbrella." And guess what? The converse could be true too: "If I see an umbrella, then it might be raining!" Just watch out for those "umbrellas just for style" situations!

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