For each of the following relations r on the set x decide whether r is reflexive, symmetric, (weakly) antisymmetric or transitive: (a) x = z, arb if and only if a ≤ b + 1; (b) x = z, arb if and only if a + b is even; (c) x = p, arb if and only if a and b are coprime: (d) x = z, arb if and only if a + b is divisible by 3; (e) x = r, arb if and only if a2 ≤ b2; (f ) x = r × r, (a, b)r(c, d) if and only if a = c; (g) x = n × n, (a, b)r(c, d) if and only if either a < c or(a = c and b ≤ d).

they can both be solutions depends on the equation

step-by-step explanation:

what is the equation? ?

faster, im not sure why but i know it is faster

1. sometimes

2.   never

3   .08c = 7.50+.05c   250 pages

step-by-step explanation:

1.   sometimes

the theoretical probability of rolling a 1 is 1/6.   perhaps you got really lucky and never rolled a 1   in those 60 times.   your experimental probability is 0.   or perhaps you rolled a 1   20 times.   your experimental probability is 20/60 is 1/3.     it really just depends on how you rolled in that experiment.

2.   never

the probability of the event occurring is 1.   that is being 100 % sure it will happen.   that is the maximum amount of confidence we have.

3.   no customer card cost:   .08 times number of pages

customer card cost:   7.50 + .05 times number of pages

we want to find when it costs the same amount, so we will set these equal

let c = number of pages

.08c = 7.50+.05c

subtract .05c from each side

.08c-.05c = 7.5+.05c-.05c

.03c=7.5

divide each side by .03

.03c/.03 = 7.5/03

c =250  

the cost is the same at 250 pages