AP CSA 2.6 Exercise 1: De Morgan, Checked

Unit 2: Selection and Iteration · Lesson 2.6 · Exercise 1

De Morgan, Checked

Comparing Boolean Expressions. Write real Java, run it, and submit it to be graded against hidden test cases.

Back to the Lesson 2.6 page All Unit 2 lessons

Why this one is worth doing

Two expressions are equivalent when they agree on every input, not when they look similar. This exercise prints both sides of two De Morgan pairs and then prints whether they matched, so equivalence stops being something you take on faith.

What to write

Read two integers, a and b.
Build p as a > 0 and q as b > 0.
Print !(p && q), then print !p || !q, which De Morgan says is the same thing.
Print whether those two agreed, as a single boolean.
Print !(p || q), then !p && !q, then whether THOSE two agreed.

Your program reads

Two integers on separate lines: a, then b.

Your program prints

Six lines of true or false: the first pair, whether it agreed, the second pair, and whether it agreed.

Worked examples

These are the cases you can see. There are more you cannot, and they use different values, so an answer that prints these numbers as constants will fail.

Example 1 input

5
3

Example 1 output

false
false
true
false
false
true

Example 2 input

-1
4

Example 2 output

true
true
true
false
false
true

Your answer

Main.java

import java.util.Scanner;

public class Main {
  public static void main(String[] args) {
    Scanner input = new Scanner(System.in);
    int a = input.nextInt();
    int b = input.nextInt();
    boolean p = a > 0;
    boolean q = b > 0;

    // Six printed booleans, in the order the task lists them.
  }
}

Input for the Run button

Run sends whatever is in the input box below. Submitting runs your program against every test case, including hidden ones with different input.

Stuck?

Hint 1

Negating a compound expression flips the operator too: not (p and q) becomes (not p) or (not q).

Hint 2

Two booleans are compared with ==, exactly like two ints. left1 == right1 is a boolean expression in its own right.

Hint 3

Lines 3 and 6 should be true for every input you can think of. If either is ever false, the expression above it is not the one De Morgan describes.

Where to go next

Rework the Lesson 2.6 page Pick another Unit 2 lesson

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