Directions: Answer these question pertaining to closure of sets. Check your answer when finished.

1.
Which of the following sets of numbers is closed under multiplication?
Choose:

 {-2, -1, 0, 1} {0, 1, 2} {-1, 0, 1, 2} {0, 1}

2.
Which of the following sets of numbers is closed under subtraction?
Choose:

 Counting Numbers Even Numbers Odd Numbers Whole Numbers

3.
Which of the following sets of numbers is not closed under addition?
Choose:

 Integers {0, 1} Even Numbers {0}

 4. Is the set {D, O, G, S} closed under the operation , as defined below? Explain. The table is read from the left column first, followed by the top row. For example D G = O.

 5. Your task is to create a new set of selected even numbers. The set is to be closed under the operation Φ defined to be a Φ b such that "a + b is a value greater than or equal to 12". Examine the picture below, and choose which numbers, of those available, can belong to your new set. Use as many of the numbers as possible.

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