At least three of the statements P-Z in the preceding problem are false. Choose

Question

At least three of the statements P-Z in the preceding problem are false. Choose any three of these false statements. For each one, carefully state a counterexample that shows the statement to be false.

P: All dogs have fleas

Q: Several dogs have fleas

R: My dog, Spike, is flea-free

S: 3 < 5

T: (n-1) + (n+1) is irrational for every positive integer n.

U: (n-1) + (n+1) is rational for every positive integer n.

V: cos(x) < 1.001 for all x > 0

W: cos(x) < 0 for all x is existent [2,3]

X: Every even integer n > 2 is the sum of two (not necessarily distinct) primes.

Y: Every set of ten distinct numbers has a largest and a smallest element.

Z: Every subset of the interval [0,1] contains a largest element.

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