To determine if R = {(0,0), (1,1), (2,2), (3,3)} is an equivalent relation on the set A = {0,1,2,3}, we need to check if it satisfies the three properties of an equivalent relation: reflexivity, symmetry, and transitivity.

1. Reflexivity: For R to be reflexive, every element in A must be related to itself. In this case, we can see that (0,0), (1,1), (2,2), and (3,3) are all present in R, which means that R is reflexive.

2. Symmetry: For R to be symmetric, if (a,b) is in R, then (b,a) must also be in R. Looking at the pairs in R, we can see that (0,0), (1,1), (2,2), and (3,3) satisfy this condition. Therefore, R is symmetric.

3. Transitivity: For R to be transitive, if (a,b) and (b,c) are in R, then (a,c) must also be in R. Since R only contains pairs of the form (x,x), there are no pairs (a,b) and (b,c) in R to check for transitivity. Therefore, R trivially satisfies the transitivity property.

Based on the above analysis, we can conclude that R = {(0,0), (1,1), (2,2), (3,3)} is an equivalent relation on the set A = {0,1,2,3}.

Question

To determine if R = {(0,0), (1,1), (2,2), (3,3)} is an equivalent relation on the set A = {0,1,2,3}, we need to check if it satisfies the three properties of an equivalent relation: reflexivity, symmetry, and transitivity.

1. Reflexivity: For R to be reflexive, every element in A must be related to itself. In this case, we can see that (0,0), (1,1), (2,2), and (3,3) are all present in R, which means that R is reflexive.

2. Symmetry: For R to be symmetric, if (a,b) is in R, then (b,a) must also be in R. Looking at the pairs in R, we can see that (0,0), (1,1), (2,2), and (3,3) satisfy this condition. Therefore, R is symmetric.

3. Transitivity: For R to be transitive, if (a,b) and (b,c) are in R, then (a,c) must also be in R. Since R only contains pairs of the form (x,x), there are no pairs (a,b) and (b,c) in R to check for transitivity. Therefore, R trivially satisfies the transitivity property.

Based on the above analysis, we can conclude that R = {(0,0), (1,1), (2,2), (3,3)} is an equivalent relation on the set A = {0,1,2,3}.

Knowee AI · Accepted Answer

To determine if R = {(0,0), (1,1), (2,2), (3,3)} is an equivalent relation on the set A = {0,1,2,3}, we need to check if it satisfies the three properties of an equivalent relation: reflexivity, symmetry, and transitivity.

1. Reflexivity: For R to be reflexive, every element in A must be related to itself. In this case, we can see that (0,0), (1,1), (2,2), and (3,3) are all present in R, which means that R is reflexive.

2. Symmetry: For R to be symmetric, if (a,b) is in R, then (b,a) must also be in R. Looking at the pairs in R, we can see that (0,0), (1,1), (2,2), and (3,3) satisfy this condition. Therefore, R is symmetric.

3. Transitivity: For R to be transitive, if (a,b) and (b,c) are in R, then (a,c) must also be in R. Since R only contains pairs of the form (x,x), there are no pairs (a,b) and (b,c) in R to check for transitivity. Therefore, R trivially satisfies the transitivity property.

Based on the above analysis, we can conclude that R = {(0,0), (1,1), (2,2), (3,3)} is an equivalent relation on the set A = {0,1,2,3}.

A = {0,1,2,3} then R = {(0,0), (1,1), (2, 2), (3,3)} is an equivalent relation on AGroup startsTrue or FalseTrue, unselectedFalse, unselected

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