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. 

Suppose that \(A\subset B\) , so \(A\) is a proper subset of \(B\). What else can you for sure conclude must be true? Select all that apply (Hint: it could help to draw a picture). Note on notation: \(S\not\subseteq T\) means “S is not a subset of T”, i.e. \(\neg (S\subseteq T)\)

Let Ai={x∈R:−i≤x≤1i}.{“version”:”1.1″,”math”:”A_i=\{x \in \mathbb{R}: -i \leq x \leq \frac{1}{i} \}.”}Find ⋃ i = 1 100 A i {“version”:”1.1″,”math”:”\bigcup_{i=1}^{100}A_i”} 

What does SIGECAPS stand for? Be sure to write in a response for each letter.

In Java, it is possible to create an infinite loop out of while and do loops but not for loops.

These two ways to set up a String will yield identical results:String my_string = new String(“123.45”);String my_string = “” + 123.45;

Refer to Code Segment 1. If x is currently 0, a = 1 and b = -1, what will x become after the statement shown is executed? 

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).

Refer to Class Definition Code Segment 3: Assume that another method has been defined that will compute and return the student’s class rank (Freshman, Sophomore, etc).  It is defined as:    public String getClassRank()Given that s1 is a student, which of the following would properly be used to get s1’s class rank? 

Which of the following reserved words in Java is used to create an instance of a class?