lexicographic order

[econ14]

Q1.Let A = {0, 1} × {0, 1} and B = {a, b, c}. Suppose A is listed in lexicographic order
based on 0 < 1 and B is in alphabetic order. If A × B × A is listed in lexicographic
order, then the next element after ((1, 0), c,(1, 1)) is
(a) ((1, 0), a,(0, 0))
(b) ((1, 1), c,(0, 0))
(c) ((1, 1), a,(0, 0))
(d) ((1, 1), a,(1, 1))
(e) ((1, 1), b,(1, 1))


Q2
Let A = {0, 1} × {0, 1} × {0, 1} and B = {a, b, c} × {a, b, c} × {a, b, c}. Suppose A
is listed in lexicographic order based on 0 < 1 and B is listed in lexicographic order
based on a < b < c. If A×B ×A is listed in lexicographic order, then the next element
after ((0, 1, 1),(c, c, c),(1, 1, 1)) is
(a) ((1, 0, 1),(a, a, b),(0, 0, 0))
(b) ((1, 0, 0),(b, a, a),(0, 0, 0))
(c) ((1, 0, 0),(a, a, a),(0, 0, 1))
(d) ((1, 0, 0),(a, a, a),(1, 0, 0))
(e) ((1, 0, 0),(a, a, a),(0, 0, 0))

[Granpa Simpson]

1) The ordering of A is as follows:
A={(0,0),(0,1),(1,0),(1,1)}
B={a,b,c}
The lexicographic ordering of AxBxA is as follows:
AxBxA={(0,0),a,(0,0)},{(0,0),a,(0,1)},{(0,0),a,(1,0)},{(0,0),a,(1,1)}......................................................{(1,1),c,(1,1)}.
Use this logic and you will get the next after {(1,0),c,(1,1)} as {(1,1),a,(0,0)}.
Others plz do check..!!!!

[Granpa Simpson]

Similarly for question 2 u will get the answer as e i.e {(1,0,0),(a,a,a),(0,0,0)}.