Compound Boolean Expressions

To be eligible to graduate from Loyola University Chicago, you must have 120 credits and a GPA of at least 2.0. C# does not use the word and. Instead it uses && (inherited from the C language). Then the requirement translates directly into C# as a compound condition:

credits >= 120 && GPA >=2.0

This is true if both credits >= 120 is true and GPA >= 2.0 is true. A short example function using this would be:

static void checkGraduation(int credits, double GPA)
{
    if (credits >= 120 && GPA >=2.0) {
        Console.WriteLine("You are eligible to graduate!");
    }
    else {
        Console.WriteLine("You are not eligible to graduate.");
    }
}

The new C# syntax for the operator &&:

condition1 && condition2

The compound condition is true if both of the component conditions are true. It is false if at least one of the conditions is false.

Suppose we want a C# condition that is true in the same situations as the mathematical expression: low < val < high. Unfortunately the math is not a C# expression. The C# operator < is binary. In C# the statement above is equivalent to

(low < val) < high

comparing a Boolean result to high, and causing a compiler error. There is a C# version. Be sure to use this pattern:

low < val && val < high

Now suppose we want the opposite condition: that val is not strictly between low and high. There are several approaches. One is that val would be less than or equal to low or greater than or equal to high. C# translate or into ||, so a C# expression would be:

val <= low || val >= high

The new C# syntax for the operator ||:

condition1 || condition2

The compound condition is true if at least one of the component conditions are true. It is false if both conditions are false.

Another logical way to express the opposite of the condition low < val < high is that it is not the case that low < val && val << high. C# translates not as !. Another way to state the condition would be

!(low < val && val < high)

The parentheses are needed because the ! operator has higher precedence than <.

A way to remember this strange not operator is to think of the use of ! in the not-equal operator: !=

The new C# syntax for the operator !:

! condition

This whole expression is true when condition is false, and false when condition is true.

Because of the precedence of !, you are often going to write:

!( condition )

Remember when such a condition is used in an if statement, outer parentheses are also needed:

if (!( condition )) {

We now have a lot of operators! Most of those in appendix Precedence of Operators have now been considered. There you can see that ! has the high precedence of unary arithmetic operators. The operators && and || are almost at the bottom of the operators considered in this book, just above the assignment operators, and below the relational operators, with && above ||. You are encourages to use parentheses to make sure.

Compound Overkill: Look back to the code converting a score to a letter grade in Multiple Tests and if-else Statements. The condition before assigning the B grade could have been:

(score >= 80 && score < 90)

That would have totally nailed the condition, but it is overly verbose in the if .. else if … code where it appeared: Since you only get to consider a B as a grade if the grade was not already set to A, the second part of the compound condition above is redundant.

There are a couple more wrinkles with compound Boolean expressions introduced later in Short-Circuiting && and ||.

Congress Exercise

A person is eligible to be a US Senator who is at least 30 years old and has been a US citizen for at least 9 years. Write a version of a program congress.cs to obtain age and length of citizenship from the user and print out if a person is eligible to be a Senator or not. A person is eligible to be a US Representative who is at least 25 years old and has been a US citizen for at least 7 years. Elaborate your program congress.cs so it obtains age and length of citizenship and prints whether a person is eligible to be a US Representative only, or is eligible for both offices, or is eligible for neither.

This exercise could be done by making an exhaustive treatment of all possible combinations of age and citizenship. Try to avoid that. (Note the paragraph just before this exercise.)

Caution: be sure to do exhaustive testing. It is easy to write code that is correct for some inputs, but not all.

Implication Exercise

We have introduced C# Boolean operators for AND, OR, and NOT. There are other Boolean operators important in logic, that are not directly given as a C# operator. One example is “implies”, also expressed in a logical if-then statement: If I am expecting rain, then I am carrying an umbrella. Otherwise put: “I am expecting rain” implies “I am carrying an umbrella”. The first part is a Boolean expression called the hypothesis, and the second part is called the conclusion. In general, when A and B are Boolean expressions, “A implies B” is also a Boolean expression.

Just as the truth of a compound Boolean expression like “A and B” depends on the truth value of the two parts, so with implies: If you are using good logic, and you start with a true assertion, you should only be able to conclude something else true, so it is true that “true implies true”. If you start with garbage you can use that false statement in a logical argument and end up with something either false or true: “false implies false” and “false implies true” are both true. The only thing that should not work is to start with something true and conclude something false. If that were the case, logical arguments would be useless, so “true implies false” is false. There is no C# operator for “implies”, but you can check all four cases of Boolean values for A and B to see that “A implies B” is true exactly when “not A or B” is true. We can express this in C# as !A || B.

So here is a silly little exercise illustrating both implication and using the C# Boolean operators: Ask the user whether “I am expecting rain” is true. (We have the UI function Agree.) Then check with the user whether “I am carrying an umbrella.” Then conclude and print out whether the implication “If I am expecting rain, then I am carrying an umbrella.” is true or not in this situation.