The reasons, whether or not the statement “ A is the set of all triangles in the plane; a ~ b if and only if a and b are congruent.” defines an equivalence relation on the set A .

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Answer 1

Question

Chapter 2.4, Problem 13E

(a)

To determine

The reasons, whether or not the statement “A is the set of all triangles in the plane; a~b if and only if a and b are congruent.” defines an equivalence relation on the set A.

(b)

To determine

The reasons, whether or not the statement “A is the set of all circles in the plane; a~b if and only if a and b have the same center.” defines an equivalence relation on the set A.

(c)

To determine

The reasons, whether or not the statement “A is the set of all straight lines in the plane; a~b if and only if a is parallel to b.” defines an equivalence relation on the set A.

(d)

To determine

The reasons, whether or not the statement “A is the set of all lines in the plane; a~b if and only if a is perpendicular to b.” defines an equivalence relation on the set A.

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Answer 2

Question

Chapter 2.4, Problem 13E

(a)

To determine

The reasons, whether or not the statement “A is the set of all triangles in the plane; a~b if and only if a and b are congruent.” defines an equivalence relation on the set A.

(b)

To determine

The reasons, whether or not the statement “A is the set of all circles in the plane; a~b if and only if a and b have the same center.” defines an equivalence relation on the set A.

(c)

To determine

The reasons, whether or not the statement “A is the set of all straight lines in the plane; a~b if and only if a is parallel to b.” defines an equivalence relation on the set A.

(d)

To determine

The reasons, whether or not the statement “A is the set of all lines in the plane; a~b if and only if a is perpendicular to b.” defines an equivalence relation on the set A.

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Answer 3

Question

Chapter 2.4, Problem 13E

(a)

To determine

The reasons, whether or not the statement “A is the set of all triangles in the plane; a~b if and only if a and b are congruent.” defines an equivalence relation on the set A.

(b)

To determine

The reasons, whether or not the statement “A is the set of all circles in the plane; a~b if and only if a and b have the same center.” defines an equivalence relation on the set A.

(c)

To determine

The reasons, whether or not the statement “A is the set of all straight lines in the plane; a~b if and only if a is parallel to b.” defines an equivalence relation on the set A.

(d)

To determine

The reasons, whether or not the statement “A is the set of all lines in the plane; a~b if and only if a is perpendicular to b.” defines an equivalence relation on the set A.

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Answer 4

Question

Chapter 2.4, Problem 13E

(a)

To determine

The reasons, whether or not the statement “A is the set of all triangles in the plane; a~b if and only if a and b are congruent.” defines an equivalence relation on the set A.

(b)

To determine

The reasons, whether or not the statement “A is the set of all circles in the plane; a~b if and only if a and b have the same center.” defines an equivalence relation on the set A.

(c)

To determine

The reasons, whether or not the statement “A is the set of all straight lines in the plane; a~b if and only if a is parallel to b.” defines an equivalence relation on the set A.

(d)

To determine

The reasons, whether or not the statement “A is the set of all lines in the plane; a~b if and only if a is perpendicular to b.” defines an equivalence relation on the set A.

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Answer 5

Chapter 2.4, Problem 13E

(a)

To determine

The reasons, whether or not the statement “A is the set of all triangles in the plane; a~b if and only if a and b are congruent.” defines an equivalence relation on the set A.

(b)

To determine

The reasons, whether or not the statement “A is the set of all circles in the plane; a~b if and only if a and b have the same center.” defines an equivalence relation on the set A.

(c)

To determine

The reasons, whether or not the statement “A is the set of all straight lines in the plane; a~b if and only if a is parallel to b.” defines an equivalence relation on the set A.

(d)

To determine

The reasons, whether or not the statement “A is the set of all lines in the plane; a~b if and only if a is perpendicular to b.” defines an equivalence relation on the set A.

Answer 6

Chapter 2.4, Problem 13E

(a)

To determine

The reasons, whether or not the statement “A is the set of all triangles in the plane; a~b if and only if a and b are congruent.” defines an equivalence relation on the set A.

Answer 7

Chapter 2.4, Problem 13E

(a)

To determine

The reasons, whether or not the statement “A is the set of all triangles in the plane; a~b if and only if a and b are congruent.” defines an equivalence relation on the set A.

Answer 8

(b)

To determine

The reasons, whether or not the statement “A is the set of all circles in the plane; a~b if and only if a and b have the same center.” defines an equivalence relation on the set A.

Answer 9

(b)

To determine

The reasons, whether or not the statement “A is the set of all circles in the plane; a~b if and only if a and b have the same center.” defines an equivalence relation on the set A.

Answer 10

(c)

To determine

The reasons, whether or not the statement “A is the set of all straight lines in the plane; a~b if and only if a is parallel to b.” defines an equivalence relation on the set A.

Answer 11

(c)

To determine

The reasons, whether or not the statement “A is the set of all straight lines in the plane; a~b if and only if a is parallel to b.” defines an equivalence relation on the set A.

Answer 12

(d)

To determine

The reasons, whether or not the statement “A is the set of all lines in the plane; a~b if and only if a is perpendicular to b.” defines an equivalence relation on the set A.

Answer 13

(d)

To determine

The reasons, whether or not the statement “A is the set of all lines in the plane; a~b if and only if a is perpendicular to b.” defines an equivalence relation on the set A.

Answer 14

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Answer 15

Expert Solution & Answer

Answer 16

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Answer 17

Ch. 2.1 - 5{x+2y|x{0,1,2},y{2,0,2}}Ch. 2.1 - 5{x+2y|x{0,1,2},y{2,0,2}}Ch. 2.1 - If A={a,b}, then bA.Ch. 2.1 - Prob. 4TFQ Ch. 2.1 - {,{}}Ch. 2.1 - {,{}}Ch. 2.1 - True/False Questions 7. Ch. 2.1 - Prob. 8TFQ Ch. 2.1 - (Assume A and B are sets). ABBA.Ch. 2.1 - If A has two elements, then P(P(A)) has eight...

The reasons, whether or not the statement “ A is the set of all triangles in the plane; a ~ b if and only if a and b are congruent.” defines an equivalence relation on the set A .

Solution Summary: The author explains that a binary relation R on set A is reflexive if (a,a)in R holds true for every triangle in A.

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The reasons, whether or not the statement “A is the set of all triangles in the plane; a~b if and only if a and b are congruent.” defines an equivalence relation on the set A.

The reasons, whether or not the statement “A is the set of all circles in the plane; a~b if and only if a and b have the same center.” defines an equivalence relation on the set A.

The reasons, whether or not the statement “A is the set of all straight lines in the plane; a~b if and only if a is parallel to b.” defines an equivalence relation on the set A.

The reasons, whether or not the statement “A is the set of all lines in the plane; a~b if and only if a is perpendicular to b.” defines an equivalence relation on the set A.

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Chapter 2 Solutions