Determine whether the relation is reflexive, symmetric, antisymmetric, and/or transitive?

Question

Question 7 of chapter relations exercise 7.1 from Discrete Mathematics and its applications by Kenneth H Rosen 7th edition:

in (c) part: for (x,y) = (1,0); x = y + 1 holds but (0,1) y = x + 1 does not

in (d) part: I know it is reflexive and transitive but how it is symmetric (as answer given in book). as for (0, 7); (7, 0) does not hold

please explain part (c) and (d) only?

Answer 1

for part c

Symmetric relation mean aRb and bRa

They say for symmetric either of definition must be satisy

so if i have (1,0 ) here it follows :x=y+1

and for (0,1) here it follow x=y-1

Hence both (1,0) and (0,1 ) are fine as symmetric relation is concerned .

Now let us see

x=y(mod7 ) which mean x=(x-y)mod7

so take (0,7) it will be x=(0-7)mod7 = -7mod7 =0------1

and take (7,0) it will be x= (7-0)mod7 = 7 mod7 = 0 -----2

From 1 and 2 both are same

Hence they are symmetric

Comments

Thanks a ton for your help! 

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No issue :D Most welcome :)