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Suppose that P => Q. Which of the following must then be true?

What is the negation of the statement P => Q?

Q => P

Q implies P

P and Not Q

P => Not Q

Not P => Not Q

What is the contrapositive of the statement P => Q?

P and Not Q

Not Q => Not P

Not P => Not Q

P => Not Q

Not P => Q

What is the negation of the statement "All cats are furry"?

All cats are not furry.

All cats are furry.

There is a cat that is furry.

There is a cat that is not furry.

What is the negation of the statement "There is a purple sheep"?

All sheep are not purple.

There is a sheep that is not purple.

All sheep are purple.

There is a purple sheep.

What is the negation of the statement "For every number n, there is some number m with m > n"?

For every number n, there is some number m with m ≤ n.

For every number n, every number m has m ≤ n.

There is some number n such that there is some number m with m ≤ n.

There is some number n such that every number m has m ≤ n.

What is the negation of the statement "There is a prime number p so that every prime number q satisfies q ≤ p"?

There is a prime number p so that every prime number q satisfies q > p.

There is a prime number p so that there is a prime number q with q > p.

For every prime number p, every prime number q satisfies q > p.

For every prime number p, there is a prime number q with q > p.