Question: Problem 4.12 Given the proposition: x IR, a real number y such that x + y = 0. a. Rewrite this proposition in English without

Problem 4.12

Given the proposition: x IR, a real number y such that x + y = 0.

a. Rewrite this proposition in English without the use of the quantifiers.

b. Find the negation of the given proposition.

Problem 4.13

Given the proposition: x IR, y IR, x + y = 0.

a. Rewrite this proposition in English without the use of the quantifiers.

b. Find the negation of the given proposition.

Problem 4.14

Consider the proposition Somebody is older than everybody. Rewrite this proposition in the form a person x such that .

Problem 4.15

Given the proposition: There exists a program that gives the correct answer to every question that is posed to it.

a. Rewrite this proposition using quantifiers and variables.

b. Find a negation for the given proposition.

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