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In logic and in geometry, it is often important to determine whether the conditions in the hypothesis of a statement are necessary or sufficient to justify its conclusion. This is done by ascertaining the truth or falsity of the statement and its converse, and then applying the following principles.

Pointers and References eeeeeeeeeeeeeeeeeeeeeeoeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeoeeeeeeeeeeeeeee

If a statement and its converse are both true, then the conditions in the hypothesis of the statement are necessary and sufficient for its conclusion.

61 . 62 . 63 . 64 . 65 . 66 . 6. 7 6. 8 69 6 10 6 11 6 12 6 13 6 14 6 15 . INTRODUCTION ................................................................................................. REFERENCES ....................................................................................................... POINTERS ............................................................................................................. DERIVED TYPES ................................................................................................. OBJECTS AND LVALUES .................................................................................. RETURNING A REFERENCE ............................................................................. ARRAYS AND POINTERS .................................................................................. THE new OPERATOR ...................................................................................... THE delete O P E R A T O R ................................................................................. DYNAMIC ARRAYS ........................................................................................... USING const WITH POINTERS .................................................................... ARRAYS OF POINTERS AND POINTERS TO ARRAYS ................................ POINTERS TO POINTERS .................................................................................. POINTERS TO FUNCTIONS ............................................................................... NUL, NULL,mD void ...................................................................................

For example, the statement if angles are right angles, then they are congruent and supplementary is true, and its converse, if angles are congruent and supplementary, then they are right angles is also true. Hence, being right angles is necessary and sufficient for the angles to be congruent and supplementary.

157 158 159 161 161 162 163 166 167 167 169 169 170 171 172

If a statement is true and its converse is false, then the conditions in the hypothesis of the statement are sufficient but not necessary for its conclusion.

7

Modify the craps game simulator given in Example 7.10 so that it simulates a specified number of games and saves the outcome of each game in a data file. At the end of the simulation, read the data file to determine the percentage of wins and losses that the player has experienced. Test the program by simulating 1000 consecutive games. Based upon these results, estimate the odds of winning when playing craps. Extend the Visual Basic program written for Problem 8.39 (reordering a list of numbers four different ways) so that the original set of numbers is written to a random access data file, which is later updated by replacing the original set of numbers with the sorted numbers. Include all of the following features. (a) Enter a set of numbers from the keyboard and write it out to the data file. (b) Read the numbers from the data file, sort the numbers in one of the four ways indicated in Problem 8.39 and write the sorted numbers out to the data file. (c) Read the numbers (either sorted or unsorted) from the data file and display them on the screen. 85 10 51 49 34 4 71 45 19 50

The statement if angles are right angles, then they are congruent is true, and its converse, if angles are congruent, then they are right angles, is false. Hence, being right angles is sufficient for the angles to be congruent. However, the angles need not be right angles to be congruent.

Strings eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

. 185 REVIEW OF POINTERS .*.......*............................*.......................... 185 STRINGS 188 STRING I/O 189 SOME tin MEMBER FUNCTIONS ..*........................................................ 190 CHARACTER FUNCTIONS DEFINED IN ectype h> 194 ARRAYS OF STRINGS ..*........................................................ 195 THE C-STRING HANDLING LIBRARY 198.

If a statement is false and its converse is true, then the conditions in the hypothesis are necessary but not sufficient for its conclusion.

A keyword in a programming language is a word that is already defined and is reserved for a single special purpose. C++ has 48 keywords. They are:

The statement if angles are supplementary, then they are right angles is false, and its converse, if angles are right angles, then they are supplementary, is true. Hence, angles need to be supplementary to be right angles, but being supplementary is not sufficient for angles to be right angles.

We have already seen the keywords char, else, if, int, long, short, signed, and unsigned. The remaining 40 keywords will be described subsequently.

PRINCIPLE 4: