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Consider the following sentence: If the product of two integers is even, then at least one of those integers must be even. 1) Write that sentence as a logical statement (quantifiers will be involved). You may use standard arithmetical symbols such as multiplication, division, etc. Ensure that your statement is a proposition. 2) Prove the statement from definitions. You may use the fact that every integer is even or odd and never both.  3) Identify that method of proof that you used. 

Write a declaration for a Rectangle named squareShape that is 400 pixels wide, 400 pixels high, and its upper-left corner position is at point (50, 50).

A GUI control sets up an event but it is the programmer who writes the code for the event handler which executes when an event occurs.

In Java, ‘a’ and ‘A’ are considered to be different values.

Java methods can only return primitive types.

Refer to Problem 1. Write a statement to guarantee that the initial will be a capital letter. Hint: use a method in the String class.

Refer to Class Definition Code Segment 3: Which of the following could be used to instantiate a new Student s1?

Consider the following code that will assign a letter grade of ‘A’, ‘B’, ‘C’, ‘D’, or ‘F’ depending on a student’s test score. if (score >= 90)    grade = ‘A’; if (score >= 80)    grade = ‘B’; if (score >= 70)    grade = ‘C’; if (score >= 60)    grade = ‘D’; else    grade = ‘F’;

Consider the following outline of a nested if-else structure which has more if clauses than else clauses.  Which of the statements below is true regarding this structure? if (condition1)    if (condition2)       statement1;    else        statement2;

What does the following code fragment do?Circle circle = new Circle(100, 100, 50);circle.setFill(Color.GREEN);Rectangle rectangle = new Rectangle(70, 70, 225, 75);rectangle.setStroke(Color.BLUE);rectangle.setStrokeWidth(2);rectangle.setFill(null);