Answer to Question #185567 in Discrete Mathematics for nellie karren

Question #185567

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


1
Expert's answer
2021-05-07T09:42:44-0400

1*1=1 is not divisible by 4, therefore "(1,1) \\notin R"

1*2=2*1=2 is not divisible by 4, therefore "(1,2),\\,(2,1) \\notin R"

1*3=3*1=3 is not divisible by 4, therefore "(1,3),\\,(3,1) \\notin R"

1*4=4*1=4 is divisible by 4, therefore "(1,4),\\,(4,1) \\in R"

1*5=5*1=5 is not divisible by 4, therefore "(1,5),\\,(5,1) \\notin R"

1*6=6*1=6 is not divisible by 4, therefore "(1,6),\\,(6,1) \\notin R"

1*7=7*1=7 is not divisible by 4, therefore "(1,7),\\,(7,1) \\notin R"

Continuing the reasoning in a similar way, we get the elements of the relation R:

"R = \\{ (1,4),\\,(4,1),\\,(2,2),\\,(2,4),\\,(4,2),\\,(2,6),\\,(6,2),\\,(3,4),\\,(4,3),\\,(4,4),"

"(4,5),\\,(4,6),\\,(4,7),\\,(5,4),\\,(6,4),\\,(7,4),\\,(6,6)\\}"

Find the inverse relation:

"{R^{ - 1}} = \\{ (y,x)|(x,y) \\in R\\} = \\{ (4,1),\\,(1,4),\\,(2,2),\\,(4,2),\\,(2,4),\\,(6,2),\\,(2,6),\\,(4,3),\\,(3,4),\\,(4,4),\\,(5,4),\\,"

"(6,4),\\,(7,4),\\,(4,5),\\,(4,6),\\,(4,7),\\,(6,6)\\}"


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