MAD 2104 Midterm: MAD 2104 FIU Exam f11k
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Prof. s. hudson: [10 pts] how many bit strings of length 7 contain at least ve 1"s , [10 pts] prove one, in the usual paragraph style, including the phrase x more than once. Avoid shortcuts, such as quoting stronger theorems about sets (see me, if in doubt about this). If a b, then b a: [5 points each] let a = {0, 1, 2}, give an example of a relation r on a, that is re exive but not symmetric. You may describe r in words, or by a clearly-labeled matrix, or (di)graph: give an example of a di erent relation r on a, that is transitive but not an equivalence relation. If either part of this problem is impossible, explain why: [10 points] find a boolean expression in sum-of-minterm form (eg dnf) for the function, F (x, y, z) = 1 if and only if x + y = 0: [15 points] answer true or false:
