2. (MS) Consider the relation R5 on P({0,1,2,3}) such that (A, B) e Rz if and only if |A| = |B|. Select all that are true: %3D 1. R5 is reflexive 2. R5 is symmetric 3. R5 is transitive 4. R5 is an equivalence relation

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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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hi there could you help me with these two questions 

2. (MS) Consider the relation R5 on P({0,1,2,3}) such that (A, B) e R5 if and only if |A| = |B|.
Select all that are true:
%3D
1. R5 is reflexive
2. R5 is symmetric
3. R5 is transitive
4. R5 is an equivalence relation
Transcribed Image Text:2. (MS) Consider the relation R5 on P({0,1,2,3}) such that (A, B) e R5 if and only if |A| = |B|. Select all that are true: %3D 1. R5 is reflexive 2. R5 is symmetric 3. R5 is transitive 4. R5 is an equivalence relation
1. (MS) Consider the relation R3 on P({0,1, 2, 3}) such that (A, B) e R3 if and only if the sum of
elements in A is equal to the sum of elements in B and if A and B are nonempty then the largest
element in A equals the largest element in B. (That is, R3 = R1 0 R2.)
Select all that are true:
1. R3 is reflexive
2. R3 is symmetric
3. R3 is transitive
4. R3 is an equivalence relation
Transcribed Image Text:1. (MS) Consider the relation R3 on P({0,1, 2, 3}) such that (A, B) e R3 if and only if the sum of elements in A is equal to the sum of elements in B and if A and B are nonempty then the largest element in A equals the largest element in B. (That is, R3 = R1 0 R2.) Select all that are true: 1. R3 is reflexive 2. R3 is symmetric 3. R3 is transitive 4. R3 is an equivalence relation
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