In Exercise 1 through 6, use P(x): x is even; Q(x): x is a prime number; R(x, y): x + y is...

In Exercise 1 through 6, use P(x): x is even; Q(x): x is a prime number; R(x, y): x + y is even. The variables x and y represent integers.

Exercise 1

Determine the truth value of each statement given in Exercises 2 through 6.

Exercise 2

Write an English sentence corresponding to each of the following.

(a)

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(b)

Exercise 3

Write an English sentence corresponding to each of the following.

(a)

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(b)

Exercise 4

Write an English sentence corresponding to each of the following.

(a)

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(b)

Exercise 5

Write an English sentence corresponding to each of the following.

(a)

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(b)

Exercise

Write each of the following in terms of P(x), Q(x), R(x, y), logical connectives, and quantifiers.

(a) Every integer is an odd integer.

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(b) The sum of any two integers is an even number.

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(c) There are no even prime numbers.

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(d) Every integer is even or a prime.