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.

Any is very appreciated! (picture is provided below)not sure how to do this at all won't lie

Will give brainliest plz hurry lexie surveyed 4 teenagers to find out approximately how many hours, per week, they read for fun, and how many siblings they have. brooke said she reads about 10 h a week for fun, and that she has 5 siblings. celia said she has 1 brother and 1 sister and reads for fun about 3 h each week. henry said he has 2 brothers and reads for fun about 30 min each week. jude said he doesn't read for fun and has 3 brothers and 3 sisters. use this information to complete the data table. express your answers as whole numbers or decimals. name hours of fun number of siblings brooke celia __ henry jude

A25- foot ladder leans against a building and reaches a point of 23.5 feet above the ground .find the angle that the ladder makes with the building