Is {1, 2, 3,4) a group under .5 (multiplication modulo 5)? if so, is it isomorphic to 24 or to z2 x z2?

Answer with step by step explanation:

We are given  that a set

Let A={1,2,3,4}

We have to prove that it is a group under modulo 5

Closed property:for all a,b belongs to A

Associative property:It is satisfied property

for all a,b,c belongs to A

Identity : Where e is identity of group

Hence, identity exist ,e=1

Inverse:

Hence, inverse exist of every element

Given set satisfied all properties of group under multiplication modulo.Therefore, givens set is a group under multiplication modulo.

It is a U(5) because a group under multiplication modulo is called U(n) group U(n)={r, gcd(r,n)=1}

We know that order of group U(n)=

Order of U(5)=4

We know that isomorphic to

p=5,n=1

U(5)isomorphic to

it would be:

c.parallelogram.

step-by-step explanation:

i found the life tables for the year 2012. 

life table of males at age 30. probability of dying between ages x and x+1

total population:  

29–30 . . . . . . . . . . . . 0.001030

30–31 . . . . . . . . . . . . 0.001061

males:  

29–30 . . . . . . . . . . . . 0.001420

30–31 . . . . . . . . . . . . 0.001448

white population

29–30 . . . . . . . . . . . . 0.001005

30–31 . . . . . . . . . . . . 0.001037

white males

29–30 . . . . . . . . . . . . 0.001372

30–31 . . . . . . . . . . . . 0.001399

non hispanic white population

29–30 . . . . . . . . . . . . 0.001083

30–31 . . . . . . . . . . . . 0.001116

non hispanic white males

29–30 . . . . . . . . . . . . 0.001477

30–31 . . . . . . . . . . . . 0.001503

jacob, non hispanic white male. 30 years old.

probability that jacob lives to be 30 years old. 

since the given probabilities are probabilities of dying, i think we simply subtract it from 1 to get the probability of living. we will use the probability of non hispanic white male.

                                          probability of living to be 30 y.o.

29 - 30 : 1 - 0.001477 = 0.998523

30 - 31 : 1 - 0.001503 = 0.998497