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.

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3. Consider the following theorem: Theorem: If n is an odd integer, then n³ is an odd integer. Note: There is an implicit universal quantifier for this theorem. Technically we could write: For all integers n, if n is an odd integer, then n³ is an odd integer. (a) Explore the statement by constructing at least three examples that satisfy the hypothesis, one of which uses a negative value. Verify the conclusion is true for each example. You do not need to write your examples formally, but your work should be easy to follow. (b) Pick one of your examples from part (a) and complete the following sentence frame: One example that verifies the theorem is when n = We see the hypothesis is true because and the conclusion is true because (c) Use the definition of odd to construct a know-show table that outlines the proof of the theorem. You do not need to write a proof at this time.

matrix 4

Please ensure that all parts of the question are answered thoroughly and clearly. Include a diagram to help explain answers. Make sure the explanation is easy to follow. Would appreciate work done written on paper. Thank you.

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

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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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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.