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  1. PS9 Q28. If A and B are sets whose intersection is B, then it must be true that:
    Answer: A =B
    However, the answer should be A is a subset of B. For instance:
    A = {1,3,5}
    B = {3}
    A n B = {3} = B not A
    You can only say the A = B iff A n B = A
    Am I missing something?

  2. Good catch! The answer appears to be missing from the shown results. I believe the correct answer, however, is that B is a subset of A if the intersection of A and B equals set B. The solution is updated and your example is shown with credits to you for highlighting the error. Good work. Keep it up.

  3. For question 17, I do not understand what the problem means when it says “closed under.” What does it mean when a number, such as the perfect squares, are “closed under” something?

    1. Great question. An operation is closed under the set when that operation (say multiplication) performed on any group of elements in the set produces a result that is also in the set. One example might be the set of integers. The set of integers are closed to addition. If I add any integer or integers to any other integer or integers the result must be an integer. Are integers closed to subtraction, multiplication, division? Can you think of any other examples of closed sets? Now try to apply that same concept to the set of perfect squares. Is there a certain operation when performed on any number of perfect squares that must also result in a perfect square?

  4. For Question 33, isn’t the “second hand” of the clock the hand that indicates the seconds. So for an hour, shouldn’t their be 60×60 seconds, which is 3600. So if r=5, and the formula for circumference is pi r squared, then 3600×10 is 36000 centimeters, right?

    1. The second hand does not make a full revolution every second which you are assuming in your calculation. It makes a revolution every minute or 60 revolutions in one hour.

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