Question(a) Given: If Geometry is Maria's favorite subject, then the dress is on sale. If the dress is on sale, then the television is broken. Which statement must also be true? If Geometry is Maria's favorite subject, then the television is broken. (b) Given: If I am in my first period class, then Karen heard the radio. I am in my first period class. Which statement must also be true? I am not in my first period class. (c) Given: If the mouse escaped from the cat, then Yolanda is a doctor. Which statement must also be true? (choose one) (choose one) If Yolanda is not a doctor, then the mouse did not escape from the cat. If Yolanda is a doctor, then the mouse escaped from the cat. If the mouse did not escape from the cat, then Yolanda is not a doctor.
Studdy Solution
For part (c), we have:
- If the mouse escaped from the cat, then Yolanda is a doctor.
We need to determine the contrapositive, which is logically equivalent to the original statement. The contrapositive of "If P, then Q" is "If not Q, then not P".
Thus, if Yolanda is not a doctor, then the mouse did not escape from the cat.
The conclusions are:
(a) If Geometry is Maria's favorite subject, then the television is broken.
(b) Karen heard the radio.
(c) If Yolanda is not a doctor, then the mouse did not escape from the cat.
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