Question

∀x∃y(x + y = 2 ∧ 2x − y =1

Answer 1

This statement is false. Let's take x=0 and put it in two equations: 1) 0+y=2, y=2 ; 2) 0-y=1, y=-1. Therefore we found at least one x=0 such that these two equations cannot have one common solution y. It proves that the statement is false.