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Determine which statements are the converse, inverse, and contrapositive of the following statement.

If it is after midnight, Anissa is sleeping.
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If Anissa is sleeping, it is not after midnight.
If Anissa is sleeping, it is after midnight.
If it is not after midnight, Anissa is sleeping.
If it is not after midnight, Anissa is not sleeping.
If Anissa is not sleeping, it is not after midnight.
Converse
Contrapositive
Inverca

User Tom Lord
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2 Answers

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17 votes

Final answer:

The converse of the original statement 'If it is after midnight, Anissa is sleeping' is 'If Anissa is sleeping, it is after midnight.' The inverse is 'If Anissa is sleeping, it is not after midnight,' and the contrapositive is 'If it is not after midnight, Anissa is not sleeping.'

Step-by-step explanation:

The original statement is 'If it is after midnight, Anissa is sleeping.' To analyze its converse, inverse, and contrapositive, we must first understand their definitions:

  • The converse of a conditional statement switches the hypothesis and the conclusion. For example, the converse of 'If P, then Q' is 'If Q, then P.'
  • The inverse of a conditional statement negates both the hypothesis and the conclusion. The inverse of 'If P, then Q' is 'If not P, then not Q.'
  • The contrapositive both switches the hypothesis with the conclusion and negates them both. The contrapositive of 'If P, then Q' is 'If not Q, then not P.'

Now let's determine the given statements:

  • If Anissa is sleeping, it is after midnight. - This is the converse.
  • If it is not after midnight, Anissa is not sleeping. - This is the contrapositive.
  • If it is not after midnight, Anissa is sleeping. - This does not correspond to converse, inverse, or contrapositive.
  • If Anissa is sleeping, it is not after midnight. - This is the inverse.
  • If Anissa is not sleeping, it is not after midnight. - This is not a standard logical equivalent of the original statement, it's just a negation of the conclusion.

User Marikit
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2.7k points
13 votes
13 votes

Answer:

1,2,4

Step-by-step explanation:

edem

User Ebi
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3.1k points