The negation of \"If Sue is Luiz\'s mother, then Ali is his cousin\" is \"If Sue

Question

The negation of "If Sue is Luiz's mother, then Ali is his cousin" is "If Sue is Luiz's mother, then Ali is not his cousin." Write negations for each of the following statements. (Assume that all variables represent fixed quantities or entities, as appropriate.) a. If P is a square, then P is a rectangle. b. If today is New Year's Eve, then tomorrow is January. c. If the decimal expansion of r is terminating, then r is rational. d. If n is prime, then n is odd or n is 2. e. If x is nonnegative, then x is positive or x is 0. f. If Tom is Ann's father, then Jim is her uncle and Sue is her aunt. g. If n is divisible by 6, then n is divisible by 2 and n is divisible by 3.

Explanation / Answer

let P and Q are two statements, the negotiation of "if P then Q" is " P and not Q"

so the negotiation of C is "the decimal expansion of r is terminating and r is not a rational."

the negotiation of g is " n is divisible by 6, however it is either not divisible by 2 or not divisible by 3"

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