Answer to Question #316075 in Discrete Mathematics for Alamanda

Question #316075

Consider the following relations on {1, 2, 3, 4}.

R1 = {(2,2), (2,3),(2,4),(3,2),(3,3),(3,4)}

R2 = {(1,1),(1,2),(2,1),(2,2),(3,3),(4,4)}

R3 = {2,4),(4,2)}

R4 = {(1,2),(2,3),(3,4)}

R5 = {(1,1),(2,2),(3,3),(4,4)}

a)   Which of these relations are reflexive? Justify your answers.

b)   Which of these relations are symmetric? Justify your answers.

c)   Which of these relations are antisymmetric? Justify your answer.

d)   Which of these relations are transitive? Justify your answers.


1
Expert's answer
2022-03-30T05:43:15-0400

"a:those\\,\\,which\\,\\,contain\\,\\,\\left( 1,1 \\right) ,\\left( 2,2 \\right) ,\\left( 3,3 \\right) ,\\left( 4,4 \\right) ,i.e.R_2,R_5\\\\b:those\\,\\,which\\,\\,contain\\,\\,\\left( a,b \\right) \\,\\,together\\,\\,with\\,\\,\\left( b,a \\right) ,i.e.R_3,R_5\\\\c:those\\,\\,for\\,\\,which\\,\\left( a,b \\right) \\in R,\\left( b,a \\right) \\in R\\Rightarrow a=b\\\\R_1-no,\\left( 2,3 \\right) \\in R_1,\\left( 3,2 \\right) \\in R_1\\\\R_2-no,\\left( 1,2 \\right) \\in R_2,\\left( 2,1 \\right) \\in R_2\\\\R_3-no,\\left( 2,4 \\right) \\in R_3,\\left( 4,2 \\right) \\in R_3\\\\R_4-yes, \\left( 1,2 \\right) \\in R_4,\\left( 2,1 \\right) \\notin R_4,\\left( 2,3 \\right) \\in R_4,\\left( 3,2 \\right) \\notin R_4,\\left( 3,4 \\right) \\in R_4,\\left( 4,3 \\right) \\notin R_4\\\\R_5-yes, no\\,\\,pairs\\,\\,\\left( a,b \\right) \\,\\,with\\,\\,a\\ne b\\\\R_4,R_5\\\\d:those\\,\\,which\\,\\,contain\\,\\,\\left( a,c \\right) \\,\\,together\\,\\,with\\,\\,\\left( a,b \\right) ,\\left( b,c \\right) ,i.e.R_1,R_2,R_5"

Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment

LATEST TUTORIALS
New on Blog
APPROVED BY CLIENTS