Let A = {0, 1, . . . , 9} and B = {a, b, . . . , z}. Consider the following set,

Question

Let A = {0, 1, . . . , 9} and B = {a, b, . . . , z}. Consider the following set, C, which is a subset of the Cartesian Product D = A × A × B × A:

C = {(4, 2, b, 1),(5, 1, a, 1),(3, 8, z, 9),(4, 2, c, 3),(1, 7, y, 4),(8, 2, e, 5), (5, 1, c, 3),(3, 7, d, 4),(1, 8, y, 2),(4, 1, d, 7),(1, 8, y, 1)}

The following questions pertain to the notion of lexicographic ordering of tuples.
(a) List the tuples of C in increasing order.
(b) List all tuples of C that are greater than (4, 2, a, 9).
(c) List any three tuples of D C that are between (3, 7, d, 4) and (4, 2, b, 1).
(d) How many tuples are there in D that are less than (3, 8, z, 9)? (Note that the set of interest here is D, not C.)

Explanation / Answer

(a)
C={(1,7,y,4), (1,8,y,1), (1,8,y,2), (3,7,d,4), (3,8,z,9), (4,1,d,7), (4,2,b,1), (4,2,c,3), (5,1,a,1), (8,2,e,5)}

(b)
{(4,2,b,1), (4,2,c,3), (5,1,a,1), (8,2,e,5)}

(c)
{(4,1,d,7)}

(d)
{(1,7,y,4), (1,8,y,1), (1,8,y,2), (3,7,d,4)}

Related Questions

Navigate

• Browse (All)
• Browse L
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.