1. Write the converse of the following conditional statement as in the form "if p, then q." "To pass the exam, it is sufficient to study for the exam."

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1. Write the converse of the following conditional statement as an English sentence
in the form "if p, then q."
"To pass the exam, it is sufficient to study for the exam."
2. Let S(x, y) be the statement "x has sent an email to y," where the domain of x and
y consists of all people. Write the following sentence as a logical expression (i.e.,
using predicates, quantifiers, and logical operators).
"There is exactly one person who has been sent an email by everyone."
3. Write the following argument in argument form (i.e., using propositions and logical
operators).
"If I don't eat dinner, then I have strange dreams. I have strange dreams when it
rains. I didn't have strange dreams. Therefore, I ate dinner and it didn't rain."
4. Write the assumption (i.e., what you suppose) in a proof by contradiction of the
following statement.
"If a group of 8 athletes have won a total of 65 trophies, then at least one of the
athletes has won at least 9 trophies."
Transcribed Image Text:1. Write the converse of the following conditional statement as an English sentence in the form "if p, then q." "To pass the exam, it is sufficient to study for the exam." 2. Let S(x, y) be the statement "x has sent an email to y," where the domain of x and y consists of all people. Write the following sentence as a logical expression (i.e., using predicates, quantifiers, and logical operators). "There is exactly one person who has been sent an email by everyone." 3. Write the following argument in argument form (i.e., using propositions and logical operators). "If I don't eat dinner, then I have strange dreams. I have strange dreams when it rains. I didn't have strange dreams. Therefore, I ate dinner and it didn't rain." 4. Write the assumption (i.e., what you suppose) in a proof by contradiction of the following statement. "If a group of 8 athletes have won a total of 65 trophies, then at least one of the athletes has won at least 9 trophies."
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