Determine whether R is reflexive, irreflexive, symmetric, asymmetric, antisymmetric, or transitive. If the relation fails to have a property, give an example showing why it fails. Let
A={1,2,3,4}
and R be a relation on the set A defined by:
R={(1,1),(2,2),(3,3),(1,2),(2,1),(1 ,4),(3,2),(3,1),(3,4),(4,2),(4,1)}

maybe i can

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560

$649.60

step-by-step explanation:

change of stock price/initial stock price on friday * total stock value = change of stock value

0.89/73.73 *x = 42.72

x=3539.04 = total stock value at initial stock price on friday .

total stock value at initial stock price on friday/ initial stock price on friday = number of shares

3539.04/73.73 = 48 shares

they own 48 shares of this stock