Mathematical Language

Two statements are equivalent if they always have the same logical value (a logical value is either "true" or "false", that is, if they are both true or are both false. The statements "$x = 3$" and "$x + 2 = 5$" are equivalent statements because if one of them is true then so is the other, and if one of them is false then so is the other. The statements "$x = 3$" and "$x^2 – 4x + 3 = 0$" are not equivalent since $x = 1$ makes the second statement true but the first one false.