Question

1. given the true statements: \if peter is a rabbit, then felix is a cat.\ \felix is not a cat.\ which statement must also be true? a. felix is a cat. b. felix is not a rabbit. c. peter is a cat. d. peter is not a rabbit. 20. what is the inverse of the statement \if it is sunny, i will go swimming\? a. if i go swimming, then it is sunny. b. if it is not sunny, i will not go swimming. c. if i do not go swimming, then it is not sunny. d. i will go swimming if, and only if, it is sunny. 21. which statement is the converse of \if two sides of a triangle are congruent, then the triangle is isosceles\? 23. what is the converse of the statement \if you used too much milk, then your cereal is soggy\? a. if your cereal is soggy, then you did not use too much milk. b. if you did not use too much milk, then your cereal is not soggy. c. if your cereal is not soggy, then you did not use too much milk. d. if your cereal is soggy, then you used too much milk. 24. which statement is the converse of the statement, \if jamie got a ticket, then jamie was speeding\? a. if jamie was speeding, then jamie got a ticket. b. if jamie did not get a ticket, then jamie was not speeding. c. if jamie got a ticket, then jamie was not speeding. d. if jamie was not speeding, then jamie did not get a ticket.

Explanation:

1. Given a conditional statement "If Peter is a rabbit, then Felix is a cat" and the fact that "Felix is not a cat". By modus tollens (if \(p

ightarrow q\) is true and \(
eg q\) is true, then \(
eg p\) is true), if \(p\) represents "Peter is a rabbit" and \(q\) represents "Felix is a cat", since \(
eg q\) is true, \(
eg p\) (Peter is not a rabbit) must be true.

1. The inverse of a conditional statement "If \(p\) then \(q\)" is "If \(

eg p\) then \(
eg q\)". Here \(p\) is "it is sunny" and \(q\) is "I will go swimming", so the inverse is "If it is not sunny, I will not go swimming".

1. The converse of a conditional statement "If \(p\) then \(q\)" is "If \(q\) then \(p\)". For "If two sides of a triangle are congruent, then the triangle is isosceles", \(p\) is "two sides of a triangle are congruent" and \(q\) is "the triangle is isosceles", so the converse is "If a triangle is isosceles, then two sides of the triangle are congruent".
2. The converse of "If \(p\) then \(q\)" is "If \(q\) then \(p\)". For "If you used too much milk, then your cereal is soggy", \(p\) is "you used too much milk" and \(q\) is "your cereal is soggy", so the converse is "If your cereal is soggy, then you used too much milk".
3. The converse of "If \(p\) then \(q\)" is "If \(q\) then \(p\)". For "If Jamie got a ticket, then Jamie was speeding", \(p\) is "Jamie got a ticket" and \(q\) is "Jamie was speeding", so the converse is "If Jamie was speeding, then Jamie got a ticket".

Answer:

1. D. Peter is not a rabbit.
2. B. If it is not sunny, I will not go swimming.
3. (No options shown completely, but should be "If a triangle is isosceles, then two sides of the triangle are congruent")
4. D. If your cereal is soggy, then you used too much milk.
5. A. If Jamie was speeding, then Jamie got a ticket.