My Assignment about problems of mathematics

1. (A=>B)∩(B=>C)<=>(A=>C) is tautological statement, prove!
Answer :
(A=>B)∩(B=>C)<=>(A=>C)
≡(A=> C)<=>(A=>C)
≡B
Because the value is B, so the statement (A=>B)∩(B=>C)<=>(A=>C) is tautology.

2. Find the ratio of x, y, and z from the equation (x+y)/5=(y+z)/6=(z+x)/7 !
Answer :
From that equation, we get
6x+y=5z...(i) 2x+7y=5z...(ii) 6x-7y=z...(iii)
Eliminate x from equation by name (i) and (iii), we get y=1/2 z.
Eliminate y from equation by name (ii) and (iii), we get x=3/4 z.
x : y : z = 3/4 z : 1/2 z : z = 3/4 : 1/2 : 1 = 3 : 2 : 4
So, the ratio of x, y, and z is 3 : 2 : 4.

Number 3, 4, and 5 i forgot the question.