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On the first run, nl is 22, n2 is 44, and n3 is 66. First max is assigned 22. Then, since 44 is greater than 22, max is assigned 44. Finally, since 66 is greater than 44, max is assigned 66, and that value is printed. On the second run, nl is 77, n2 is 33, and n3 is 55. First max is assigned 77. Then, since 33 is not greater than 77, max is unchanged. Finally, since 55 is also not greater than 77, max is again unchanged, and so the value 77 is printed.

1. Logically equivalent statements are at diagonally opposite vertices. Thus, the logically equivalent pairs of statements are (a) a statement and its contrapositive, and (b) the inverse and converse of the same statement. 2. Statements that are not logically equivalent are at adjacent vertices. Thus, pairs of statements that are not logically equivalent are (a) a statement and its inverse, (b) a statement and its converse, (c) the converse and contrapositive of the same statement, and (d) the inverse and contrapositive of the same statement.

2.5 COMPOUND STATEMENTS A compound statement is a sequence of statements that is treated as a single statement. C++ identifies a compound statement by enclosing its sequence of statements in curly braces. The next example contains the following compound statement:

Converse of a statement State the converse of each of the following statements, and indicate whether or not it is true. (a) Supplementary angles are two angles the sum of whose measures is 180 . (b) A square is a parallelogram with a right angle. (c) A regular polygon is an equilateral and equiangular polygon.

int temp = x; x = y; Y = temp;

CHAP. 9]

(a) Two angles the sum of whose measures is 180 are supplementary. (True) (b) A parallelogram with a right angle is a square. (False) (c) An equilateral and equiangular polygon is a regular polygon. (True)

The braces that enclose the three statements form a block. As a compound statement, it itself qualifies as a statement and can be used wherever any other statement could be used. (Note that an entire C++ program-everything that follows main ( > -forms a compound statement.)

Negative of a statement State the negative of (a) a b; (b) m B m C; (c) does not lie on the line.

EXAMPLE 2.9 Sorting This program reads two integers and then outputs them in increasing order:

main0 int x, y; tout cc "Enter two tin >> x >> y; if (x > Y> 1 int temp = x; x = y; Y = temp; tout cc x cc 1

Inverse of a statement State the inverse of each of the following statements, and indicate whether or not it is true. (a) A person born in the United States is a citizen of the United States. (b) A sculptor is a talented person. (c) A triangle is a polygon.

integers:

(a) A person who is not born in the United States is not a citizen of the United States. (False, since there are naturalized citizens) (b) One who is not a sculptor is not a talented person. (False, since one may be a fine musician, etc.) (c) A figure that is not a triangle is not a polygon. (False, since the figure may be a quadrilateral, etc.)

u << y << endl;

14.6 Forming the converse, inverse, and contrapositive State the converse, inverse, and contrapositive of the statement a square is a rectangle. Determine the truth or falsity of each, and check the logical equivalence of the statement and its contrapositive, and of the converse and inverse.