For the following program segment, m and n are integer variables. The variable A is a two-dimensional array A[1, 1], A[1, 2], . . . , A[1, 20], . . ., A[10, 1], . . . , A[10, 20], with 10 rows (indexed from 1 to 10) and 20 columns (indexed from 1 to 20).
for m : = 1 to 10 do
for n : = 1 to 20 do
A [m, n] : = m + 3 * n
Write the following statements in symbolic form. (The universe for the variable m contains only the integers from 1 to 10 inclusive; for n the universe consists of the integers from 1 to 20 inclusive.)
(a) All entries of A are positive.
(b) All entries of A are positive and less than or equal to 70.
(c) Some of the entries of A exceed 60.
(d) The entries in each row of A are sorted into (strictly) ascending order.
(e) The entries in each column of A are sorted into (strictly) ascending order.
(f) The entries in the first three rows of A are distinct.