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Chapter 3: Problem 5

Write the negation of each conditional statement. If he doesn't, I will.

Short Answer

Expert verified
The negation of 'If he doesn't, I will.' can be 'Even if he doesn't, I won't.' or 'Even if he does, I will.'

Step by step solution

01

Understanding the Conditional Statement

The original statement is: 'If he doesn't, I will.' To begin, first understand the conditional statement. It implies that the action (to be performed by you) depends on him not performing the action.
02

Negating the Conditional Statement

Next, negate the conditional. When negating a conditional, 'if...then..' becomes 'even if...still...' The negation of a conditional statement is formed either by keeping the first clause true and making the second false, or vice versa.
03

Forming the Negated Statement

Therefore, the negation of the given statement 'If he doesn't, I will.' can be 'Even if he doesn't, I won't.' or 'Even if he does, I will.' The first negation means that even if he doesn't perform the action, you aren't going to either. The second one implies that even if he does perform the action, you're still going to do it too.

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Most popular questions from this chapter

Translate each argument into symbolic form. Then determine whether the argument is valid or invalid. You may use a truth table or, if applicable, compare the argument's symbolic form to a standard valid or invalid form. (You can ignore differences in past, present, and future tense.) If I watch Schindler's List and Milk, I am aware of the destructive nature of intolerance. Today I did not watch Schindler's List or I did not watch Milk. \(\therefore\) Today I am not aware of the destructive nature of intolerance.

Translate each argument into symbolic form. Then determine whether the argument is valid or invalid. It is the case that \(x<3\) or \(x>10\), but \(x \leq 10\), so \(x<3\).

Use Euler diagrams to determine whether each argument is valid or invalid. All cowboys live on ranches. All cowherders live on ranches. Therefore, all cowboys are cowherders.

This is an excerpt from a 1967 speech in the U.S. House of Representatives by Representative Adam Clayton Powell: He who is without sin should cast the first stone. There is no one here who does not have a skeleton in his closet. I know, and I know them by name. Powell's argument can be expressed as follows: No sinner is one who should cast the first stone. All people here are sinners. Therefore, no person here is one who should cast the first stone. Use an Euler diagram to determine whether the argument is valid or invalid.

Use Euler diagrams to determine whether each argument is valid or invalid. All humans are warm-blooded. No reptiles are warm-blooded. Therefore, no reptiles are human.
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