Solution to Let R be the relation on the set A = {1, 2, 3, 4, 5, … - Sikademy
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Archangel Macsika

Let R be the relation on the set A = {1, 2, 3, 4, 5, 6, 7} defined by the rule if the integer (a – b) is divisible by 4. List the elements of R and its inverse?

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Let R be the relation on the set A =\{1, 2, 3, 4, 5, 6, 7\} defined by the rule if the integer (a -b) is divisible by 4. Let us list the elements of R:

R=\{(1,5),(5,1),(2,6),(6,2),(3,7),(7,3)\}.


It follows from (a,b)\in R that (a -b) is divisible by 4, and hence (b -a)=-(a-b) is also divisible by 4. Consequently, (b,a)\in R. We conclude that the for the inverse relation we have R^{-1}=\{(a,b)\ | \ (b,a)\in R\}=R.

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Question ID: mtid-5-stid-8-sqid-3205-qpid-1904