Let k, be a theory whose language has only = as a predicate letter and no function letters or individual constants. let its proper axioms be (vx1)x1 = x1, (vxl)(vx2)(x2 = x2 * x2 = xı), and (vx1)(vx2)(vx3)(x1 = x2 = (x2 = xz x1 = x; show that k is a theory with equality. (hint: it suffices to prove that + xy = x3 = (x2 = x2 = x3 = x,) and x2 = x3 = (x1 = x2 = x2 = x3).] k, is called the pure first-order theory of equality.

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answer: i realy don't get it that much can you me figer it out pleas you

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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

i can not answer the question due to the fact that you spelled "carton" as "cartoon", a cartoon is something you watch on tv, a carton is a box that holds things. and also you've been waiting for this question for a while so why don't you get off your lazy a** and try to figure it out for yourself for once!

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look above, and leave your comments down below, and don't for get a five stars and a and brainliest xd

sorry for the stars in the middle of words its because it wouldn't let me submit. xd