Uncomparable Puzzles in Java

This is a few puzzles for you to solve in Java.

b == a is true
(long) b < a is true

d < c is true
d < (long) c is false

e <= f is true
e >= f is true
e == f is false

x == y is false
x.doubleValue() == y.doubleValue() is true
x.equals(y) is false
x.compareTo(y) == 0 is true

long a = (1L << 54) + 1;
double b = a;
System.out.println("b == a is " + (b == a));
System.out.println("(long) b < a is " + ((long) b < a));

double c = 1e19;
long d = 0;
d += c;
System.out.println("\nd < c is " + (d < c));
System.out.println("d < (long) c is " + (d < (long) c));

Double e = 0.0;
Double f = 0.0;
System.out.println("\ne <= f is " + (e <= f));
System.out.println("e >= f is " + (e >= f));
System.out.println("e == f is " + (e == f));

BigDecimal x = new BigDecimal("0.0");
BigDecimal y = BigDecimal.ZERO;
System.out.println("\nx == y is " + (x == y));
System.out.println("x.doubleValue() == y.doubleValue() is " + (x.doubleValue() == y.doubleValue()));
System.out.println("x.equals(y) is " + x.equals(y));
System.out.println("x.compareTo(y) == 0 is " + (x.compareTo(y) == 0));

List<BigDecimal> bds = Arrays.asList(new BigDecimal("1"), 
    new BigDecimal("1.0"), new BigDecimal("1.00"), BigDecimal.ONE);
System.out.println("bds.size()=    " + bds.size());
Set<BigDecimal>bdSet = new HashSet<>(bds);
System.out.println("bdSet.size()=  " + bdSet.size());
Set<BigDecimal>bdSet2 = new TreeSet<>(bds);
System.out.println("bdSet2.size()= " + bdSet2.size());

bds.size()=    4
bdSet.size()=  3
bdSet2.size()= 1