91Ó°ÊÓ

Are the following statments true or false? If the statement is true, prove it; if it is false, give a counterexample showing it is false. (a) "If \(\phi_{1}, \phi_{2}\) are linearly independent functions on an interval \(I\), they are linearly independent on any interval \(J\) contained inside \(I\) " (b) "If \(\phi_{1}, \phi_{2}\) are linearly dependent on an interval \(I\), they are linearly dependent on any interval \(J\) contained inside \(I\) " (c) "If \(\phi_{1}, \phi_{2}\) are linearly independent solutions of \(L(y)=0\) on an interval \(I\), they are linearly independent on any interval \(J\) contained inside \(I\) "" (d) "If \(\phi_{1}, \phi_{2}\) are linearly dependent solutions of \(L(y)=0\) on an interval \(I\), they are linearly dependent on any interval \(J\) contained inside \(I\) ""