Proposition. for all integers x, y, and z, if x|y and y z, then x|z proof. let a, b, and c be arbitrary integers. suppose that alb and b|c. since a|b, there is an integer whose product with a is b. let n be such an integer, so a xn = b. since bc, there is an integer whose product with b is c. let m be such an integer, so integer bxm 3 с. тhus, c 3d b x m %3 (а х п) х т %3d ах (n m). since n x m is an a c. since a, b, and c were arbitrary, we have an integer whose product with a is c, so we have proved the proposition in the video, we gave a partial natural deduction formalization of this proof. give a full formalization, yourself to the assumption vavyvz (xx y) x z xx (yxz)

In a recent basketball game between the storm and the chargers, the number of points scored by the storm in the first half was equal to the number of points scored by the chargers in the second half of the game. in the first half, the storm scored 64 points, which is one - third of the total points that were scored during the game. during the second half, the chargers scored 16 points more than one - fourth the points scored in the game. you want to know how many total points that were scored during the game. 1. write an equation that models this situation. then, solve the equation. 2. how many total points were scored during the game? explain your reasoning. 3. does your answer make sense? justify your reasoning.

Find the solution of system of equation y= x-4 y=4x+2

Find the greatest common factor of the followig monomials 46g^2h and 34g^6h^6