public class gates
{
 public static boolean and(boolean a, boolean b)
  {return(a && b);}

 public static boolean or(boolean a, boolean b)
  {return(a || b);}

 public static boolean not(boolean a)
  {return(!a);}

 public static boolean nor(boolean a, boolean b)
 {return(not(or(a,b)));}

 public static boolean nand(boolean a, boolean b)
 {return(not(and(a,b)));}

 public static boolean implies(boolean a, boolean b)
 {return(or(not(a),b));}

 public static boolean xor(boolean a, boolean b)
  {return(or(and(not(a),b),and(a,not(b))));}

 public static boolean equiv(boolean a, boolean b)
  {return(or(and(not(a),not(b)),and(a,b)));}
}