The truth value and explain the answer for symbolic statement ∀ x ∀ y p ( x , y ) If the statement is FALSE, give a counter example. Let the universe for both variables x and y be the set { 1 , 2 , 3 , 4 , 5 , 6 } and also p ( x , y ) = “ x divides y ”.

Question

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Answer 1

Question

Chapter 11.6, Problem 15E

(a)

To determine

The truth value and explain the answer for symbolic statement ∀x∀yp(x,y) If the statement is FALSE, give a counter example. Let the universe for both variables x and y be the set {1,2,3,4,5,6} and also p(x,y) = “x divides y”.

(b)

To determine

The truth value and explain the answer for symbolic statement ∀x∃yp(x,y) If the statement is FALSE, give a counter example. Let the universe for both variables x and y be the set {1,2,3,4,5,6} and also p(x,y) = “x divides y”.

(c)

To determine

The truth value and explain the answer for symbolic statement ∃x∀yp(x,y).

If the statement is FALSE, give a counter example. Let the universe for both variables x and y be the set {1,2,3,4,5,6} and also p(x,y) = “x divides y”.

(d)

To determine

The truth value and explain the answer for symbolic statement ∃y∀xp(x,y).

If the statement is FALSE, give a counter example. Let the universe for both variables x and y be the set {1,2,3,4,5,6} and also p(x,y) = “x divides y”.

(e)

To determine

The truth value and explain the answer for symbolic statement ∀y∃xp(x,y).

If the statement is FALSE, give a counter example. Let the universe for both variables x and y be the set {1,2,3,4,5,6} and also p(x,y) = “x divides y”.

(f)

To determine

The truth value and explain the answer for symbolic statement ∀xp(x,x).

If the statement is FALSE, give a counter example.

Expert Solution & Answer

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Answer 2

Question

Chapter 11.6, Problem 15E

(a)

To determine

The truth value and explain the answer for symbolic statement ∀x∀yp(x,y) If the statement is FALSE, give a counter example. Let the universe for both variables x and y be the set {1,2,3,4,5,6} and also p(x,y) = “x divides y”.

(b)

To determine

The truth value and explain the answer for symbolic statement ∀x∃yp(x,y) If the statement is FALSE, give a counter example. Let the universe for both variables x and y be the set {1,2,3,4,5,6} and also p(x,y) = “x divides y”.

(c)

To determine

The truth value and explain the answer for symbolic statement ∃x∀yp(x,y).

If the statement is FALSE, give a counter example. Let the universe for both variables x and y be the set {1,2,3,4,5,6} and also p(x,y) = “x divides y”.

(d)

To determine

The truth value and explain the answer for symbolic statement ∃y∀xp(x,y).

If the statement is FALSE, give a counter example. Let the universe for both variables x and y be the set {1,2,3,4,5,6} and also p(x,y) = “x divides y”.

(e)

To determine

The truth value and explain the answer for symbolic statement ∀y∃xp(x,y).

If the statement is FALSE, give a counter example. Let the universe for both variables x and y be the set {1,2,3,4,5,6} and also p(x,y) = “x divides y”.

(f)

To determine

The truth value and explain the answer for symbolic statement ∀xp(x,x).

If the statement is FALSE, give a counter example.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 11.6, Problem 15E

(a)

To determine

The truth value and explain the answer for symbolic statement ∀x∀yp(x,y) If the statement is FALSE, give a counter example. Let the universe for both variables x and y be the set {1,2,3,4,5,6} and also p(x,y) = “x divides y”.

(b)

To determine

The truth value and explain the answer for symbolic statement ∀x∃yp(x,y) If the statement is FALSE, give a counter example. Let the universe for both variables x and y be the set {1,2,3,4,5,6} and also p(x,y) = “x divides y”.

(c)

To determine

The truth value and explain the answer for symbolic statement ∃x∀yp(x,y).

If the statement is FALSE, give a counter example. Let the universe for both variables x and y be the set {1,2,3,4,5,6} and also p(x,y) = “x divides y”.

(d)

To determine

The truth value and explain the answer for symbolic statement ∃y∀xp(x,y).

If the statement is FALSE, give a counter example. Let the universe for both variables x and y be the set {1,2,3,4,5,6} and also p(x,y) = “x divides y”.

(e)

To determine

The truth value and explain the answer for symbolic statement ∀y∃xp(x,y).

If the statement is FALSE, give a counter example. Let the universe for both variables x and y be the set {1,2,3,4,5,6} and also p(x,y) = “x divides y”.

(f)

To determine

The truth value and explain the answer for symbolic statement ∀xp(x,x).

If the statement is FALSE, give a counter example.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 11.6, Problem 15E

(a)

To determine

The truth value and explain the answer for symbolic statement ∀x∀yp(x,y) If the statement is FALSE, give a counter example. Let the universe for both variables x and y be the set {1,2,3,4,5,6} and also p(x,y) = “x divides y”.

(b)

To determine

The truth value and explain the answer for symbolic statement ∀x∃yp(x,y) If the statement is FALSE, give a counter example. Let the universe for both variables x and y be the set {1,2,3,4,5,6} and also p(x,y) = “x divides y”.

(c)

To determine

The truth value and explain the answer for symbolic statement ∃x∀yp(x,y).

If the statement is FALSE, give a counter example. Let the universe for both variables x and y be the set {1,2,3,4,5,6} and also p(x,y) = “x divides y”.

(d)

To determine

The truth value and explain the answer for symbolic statement ∃y∀xp(x,y).

If the statement is FALSE, give a counter example. Let the universe for both variables x and y be the set {1,2,3,4,5,6} and also p(x,y) = “x divides y”.

(e)

To determine

The truth value and explain the answer for symbolic statement ∀y∃xp(x,y).

If the statement is FALSE, give a counter example. Let the universe for both variables x and y be the set {1,2,3,4,5,6} and also p(x,y) = “x divides y”.

(f)

To determine

The truth value and explain the answer for symbolic statement ∀xp(x,x).

If the statement is FALSE, give a counter example.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 5

Chapter 11.6, Problem 15E

(a)

To determine

The truth value and explain the answer for symbolic statement ∀x∀yp(x,y) If the statement is FALSE, give a counter example. Let the universe for both variables x and y be the set {1,2,3,4,5,6} and also p(x,y) = “x divides y”.

(b)

To determine

The truth value and explain the answer for symbolic statement ∀x∃yp(x,y) If the statement is FALSE, give a counter example. Let the universe for both variables x and y be the set {1,2,3,4,5,6} and also p(x,y) = “x divides y”.

(c)

To determine

The truth value and explain the answer for symbolic statement ∃x∀yp(x,y).

If the statement is FALSE, give a counter example. Let the universe for both variables x and y be the set {1,2,3,4,5,6} and also p(x,y) = “x divides y”.

(d)

To determine

The truth value and explain the answer for symbolic statement ∃y∀xp(x,y).

If the statement is FALSE, give a counter example. Let the universe for both variables x and y be the set {1,2,3,4,5,6} and also p(x,y) = “x divides y”.

(e)

To determine

The truth value and explain the answer for symbolic statement ∀y∃xp(x,y).

If the statement is FALSE, give a counter example. Let the universe for both variables x and y be the set {1,2,3,4,5,6} and also p(x,y) = “x divides y”.

(f)

To determine

The truth value and explain the answer for symbolic statement ∀xp(x,x).

If the statement is FALSE, give a counter example.

Answer 6

Chapter 11.6, Problem 15E

(a)

To determine

The truth value and explain the answer for symbolic statement ∀x∀yp(x,y) If the statement is FALSE, give a counter example. Let the universe for both variables x and y be the set {1,2,3,4,5,6} and also p(x,y) = “x divides y”.

Answer 7

Chapter 11.6, Problem 15E

(a)

To determine

The truth value and explain the answer for symbolic statement ∀x∀yp(x,y) If the statement is FALSE, give a counter example. Let the universe for both variables x and y be the set {1,2,3,4,5,6} and also p(x,y) = “x divides y”.

Answer 8

(b)

To determine

The truth value and explain the answer for symbolic statement ∀x∃yp(x,y) If the statement is FALSE, give a counter example. Let the universe for both variables x and y be the set {1,2,3,4,5,6} and also p(x,y) = “x divides y”.

Answer 9

(b)

To determine

The truth value and explain the answer for symbolic statement ∀x∃yp(x,y) If the statement is FALSE, give a counter example. Let the universe for both variables x and y be the set {1,2,3,4,5,6} and also p(x,y) = “x divides y”.

Answer 10

(c)

To determine

The truth value and explain the answer for symbolic statement ∃x∀yp(x,y).

If the statement is FALSE, give a counter example. Let the universe for both variables x and y be the set {1,2,3,4,5,6} and also p(x,y) = “x divides y”.

Answer 11

(c)

To determine

The truth value and explain the answer for symbolic statement ∃x∀yp(x,y).

If the statement is FALSE, give a counter example. Let the universe for both variables x and y be the set {1,2,3,4,5,6} and also p(x,y) = “x divides y”.

Answer 12

(d)

To determine

The truth value and explain the answer for symbolic statement ∃y∀xp(x,y).

If the statement is FALSE, give a counter example. Let the universe for both variables x and y be the set {1,2,3,4,5,6} and also p(x,y) = “x divides y”.

Answer 13

(d)

To determine

The truth value and explain the answer for symbolic statement ∃y∀xp(x,y).

If the statement is FALSE, give a counter example. Let the universe for both variables x and y be the set {1,2,3,4,5,6} and also p(x,y) = “x divides y”.

Answer 14

(e)

To determine

The truth value and explain the answer for symbolic statement ∀y∃xp(x,y).

If the statement is FALSE, give a counter example. Let the universe for both variables x and y be the set {1,2,3,4,5,6} and also p(x,y) = “x divides y”.

Answer 15

(e)

To determine

The truth value and explain the answer for symbolic statement ∀y∃xp(x,y).

If the statement is FALSE, give a counter example. Let the universe for both variables x and y be the set {1,2,3,4,5,6} and also p(x,y) = “x divides y”.

Answer 16

(f)

To determine

The truth value and explain the answer for symbolic statement ∀xp(x,x).

If the statement is FALSE, give a counter example.

Answer 17

(f)

To determine

The truth value and explain the answer for symbolic statement ∀xp(x,x).

If the statement is FALSE, give a counter example.

Answer 18

Expert Solution & Answer

Answer 19

Expert Solution & Answer

Answer 20

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Check out a sample textbook solution

See solution

Answer 21

Ch. 11.1 - Determine which of the following sentences are...Ch. 11.1 - Prob. 2CYU Ch. 11.1 - Prob. 1E Ch. 11.1 - In Exercises 1–15, determine which sentences are...Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - In Exercises 115, determine which sentences are...Ch. 11.1 - Prob. 8E

The truth value and explain the answer for symbolic statement ∀ x ∀ y p ( x , y ) If the statement is FALSE, give a counter example. Let the universe for both variables x and y be the set { 1 , 2 , 3 , 4 , 5 , 6 } and also p ( x , y ) = “ x divides y ”.

Solution Summary: The author explains the truth value of symbolic statement forall x and yp(x,y).

Concept explainers

Videos

The truth value and explain the answer for symbolic statement ∀x∀yp(x,y) If the statement is FALSE, give a counter example. Let the universe for both variables x and y be the set {1,2,3,4,5,6} and also p(x,y) = “x divides y”.

The truth value and explain the answer for symbolic statement ∀x∃yp(x,y) If the statement is FALSE, give a counter example. Let the universe for both variables x and y be the set {1,2,3,4,5,6} and also p(x,y) = “x divides y”.

The truth value and explain the answer for symbolic statement ∃x∀yp(x,y).

If the statement is FALSE, give a counter example. Let the universe for both variables x and y be the set {1,2,3,4,5,6} and also p(x,y) = “x divides y”.

The truth value and explain the answer for symbolic statement ∃y∀xp(x,y).

If the statement is FALSE, give a counter example. Let the universe for both variables x and y be the set {1,2,3,4,5,6} and also p(x,y) = “x divides y”.

The truth value and explain the answer for symbolic statement ∀y∃xp(x,y).

If the statement is FALSE, give a counter example. Let the universe for both variables x and y be the set {1,2,3,4,5,6} and also p(x,y) = “x divides y”.

The truth value and explain the answer for symbolic statement ∀xp(x,x).

If the statement is FALSE, give a counter example.

Want to see the full answer?

Chapter 11 Solutions

The truth value and explain the answer for symbolic statement ∀ x ∀ y p ( x , y ) If the statement is FALSE, give a counter example. Let the universe for both variables x and y be the set { 1 , 2 , 3 , 4 , 5 , 6 } and also p ( x , y ) = “ x divides y ”.

Solution Summary: The author explains the truth value of symbolic statement forall x and yp(x,y).

Concept explainers

Videos

The truth value and explain the answer for symbolic statement ∀x∀yp(x,y) If the statement is FALSE, give a counter example. Let the universe for both variables x and y be the set {1,2,3,4,5,6} and also p(x,y) = “x divides y”.

The truth value and explain the answer for symbolic statement ∀x∃yp(x,y) If the statement is FALSE, give a counter example. Let the universe for both variables x and y be the set {1,2,3,4,5,6} and also p(x,y) = “x divides y”.

The truth value and explain the answer for symbolic statement ∃x∀yp(x,y). If the statement is FALSE, give a counter example. Let the universe for both variables x and y be the set {1,2,3,4,5,6} and also p(x,y) = “x divides y”.

The truth value and explain the answer for symbolic statement ∃y∀xp(x,y). If the statement is FALSE, give a counter example. Let the universe for both variables x and y be the set {1,2,3,4,5,6} and also p(x,y) = “x divides y”.

The truth value and explain the answer for symbolic statement ∀y∃xp(x,y). If the statement is FALSE, give a counter example. Let the universe for both variables x and y be the set {1,2,3,4,5,6} and also p(x,y) = “x divides y”.

The truth value and explain the answer for symbolic statement ∀xp(x,x). If the statement is FALSE, give a counter example.

Want to see the full answer?

Chapter 11 Solutions

The truth value and explain the answer for symbolic statement ∃x∀yp(x,y).

If the statement is FALSE, give a counter example. Let the universe for both variables x and y be the set {1,2,3,4,5,6} and also p(x,y) = “x divides y”.

The truth value and explain the answer for symbolic statement ∃y∀xp(x,y).

If the statement is FALSE, give a counter example. Let the universe for both variables x and y be the set {1,2,3,4,5,6} and also p(x,y) = “x divides y”.

The truth value and explain the answer for symbolic statement ∀y∃xp(x,y).

If the statement is FALSE, give a counter example. Let the universe for both variables x and y be the set {1,2,3,4,5,6} and also p(x,y) = “x divides y”.

The truth value and explain the answer for symbolic statement ∀xp(x,x).

If the statement is FALSE, give a counter example.