p.641, icon at Example 9 # 1. Let A be the set of real numbers, and R be the equivalence relation R where xRy if and only if x-y is an integer. (Example 2 in the textbook confirms that R is an equivalence relation.) Find the equivalence classes of 0, 1, 1.5 and 1.7. How many equivalence classes are there?

Question 38 The correct statements are: If If Σ □ If If Ø, then Σ* has a subset that is not regular. Ø, then Σ* has a subset that is not context free. Ø, then Σ* has a subset that is not in D. Ø, then Σ* has a subset that is not in SD.

in C++, for classes with pointer member variables, you should include the copy constructor and the ____________________ in the class.

Please use Python when answering this question:  Also could you please run a doctest for each solution in the output to make sure the code works and returns everything in the output.  Write a function numPairs that accepts two arguments, a target number and a list of numbers. The function then returns the count of pairs of numbers from the list that sum to the target number. In the first example the answer is 2 because the pairs (0,3) and (1,2) both sum to 3. The pair can be two of the same number, e.g. (2,2) but only if the two 2’s are separate twos in the list. In the last example below, there are three 2’s, so there are three different pairs (2,2) so there are 5 pairs total that sum to 4. output:  >>> numPairs( 3, [0,1,2,3] ) 2    >>> numPairs( 4, [0,1,2,3] ) 1   >>> numPairs( 6, [0,1,2,3] ) 0   >>>numPairs( 4, [0,1,2,3,4,2] ) 3   >>> numPairs( 4, [0,1,2,3,4,2,2] ) 5   >>> numPairs( 4, [0,1,2,3,4,2,2] )==5 TRUE