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Which of the following binary operations are closeda.

Chapter 2, Problem 1E

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QUESTION:

Which of the following binary operations are closed?

a. subtraction of positive integers

b. division of nonzero integers

c. function composition of polynomials with real coefficients

d. multiplication of 2 X 2 matrices with integer entries

Questions & Answers

QUESTION:

Which of the following binary operations are closed?

a. subtraction of positive integers

b. division of nonzero integers

c. function composition of polynomials with real coefficients

d. multiplication of 2 X 2 matrices with integer entries

ANSWER:

Step 1 of 4

a) The set of positive integers is not a close set for subtraction since  but  hence  but  so although  and , .

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