Find mathematical sentences P and Q such that P rightarrow Q

Find mathematical sentences P and Q such that P rightarrow Q is true, but the converse, Q rightarrow P, is false.

Solution

1) Let P= \'x\' is an integer

Q= \'x\' is a Real number then P=> Q is true but converse Q=>P is False.

2) P= Function f(x) is differentianble in (a, b)

Q= f(x) is continuous in [a, b] then P=> Q is true but converse Q=>P is False.