In each case below, a relation on the set {1, 2, 3} is given. of the three properties, reflexivity, symmetry, and transitivity, determine which ones the relation has. give reasons.

a. is symmetric but not reflexive and transitive

b. is reflexive and transitive but not symmetric

c. is reflexive, symmetric and transitive

Step-by-step explanation:

The cases are missing in the question.

Let the cases be as follows:

a. R = {(1, 3), (3, 1), (2, 2)}

b. R = {(1, 1), (2, 2), (3, 3), (1, 2)}

c. R = ∅

R is defined on the set {1, 2, 3}

a.  R = {(1, 3), (3, 1), (2, 2)} is

b. R = {(1, 1), (2, 2), (3, 3), (1, 2)} is

is reflexive because (1, 1), (2, 2), (3, 3) is in R

is not symmetric because for (1,2) (2,1) is not in R

is transitive becaue for (1,1) and (1,2) we have (1,2) in R

c. R = ∅ is

reflexive, symmetric and transitive because it satisfies the definitions since there is no counter example.

wholesale price is the initial price before markup. retail price comes after the markup.

a price of 8 bucks that's marked up by 100%   is

formula: initial price + (percent markup in fraction/decimal)(initial price)

8+(1)(8)

8+8

16

retail price is $16.

dc=6 square root of 3 and ac is 12 square root 3

c and d

step-by-step explanation:

square root of 3/2 = 18/c

cross multiply to get 18*2=√3*c

36/√3 * √3/√3 = c

c= 36*√3/3

c=12√3