, contrapositive of “ if f (x1) = f (x2),
then x1 = x2” is “if x1 ≠x2, then  f (x1) ≠ f (x2)” Now
x1 ≠ x2
⇒
2x1 ≠ 2x2
⇒
2x1+ 5 ≠ 2x2 + 5
⇒
f (x1) ≠ f (x2) Since “~ q ⇒ ~ p”, is equivalent to “p ⇒ q” the proof is complete Example 7 Show that “if a matrix A is invertible, then A is non singular”