Show that the two sentences below are logically equivalent. Express each pair of sentences using a logical expression. Then prove whether the two expressions are logically equivalent. Note: you can assume that x and y are real numbers, so if x is not irrational, then x is rational, and if x is not rational, then x is an irrational number.

• If x is a rational number and y is an irrational number then x-y is an irrational number.
• If x is a rational number and x-y is a rational number then y is a rational number.