Exercise3.12(a) Show that the bridge numberb(K)of a nontrivial knotKis always less than or equal to the least number of crossings in any projection of the knot. (Hint: It may help to think about the cases where the projection is alternating or nonalternating separately.) (b)* Show that the bridge numberb(K)of a nontrivial knotKis strictly less than the least number of crossings in any projection of the knot.