IST230 Lesson 7 quiz

IST230 Lesson 7 quiz

Question
	
1. (Counts Double)



Let
A be the set of all students who enjoy solving puzzles















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Let
B be the set of all students who do well in IST 230



Now
use the following “facts” to give a formal proof that A = B (Hint: remember you
must prove two separate things). The “facts” are:



(1) If a student is a good
problem solver, then the student does well in IST 230






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(2) If a student enjoys
solving puzzles, then the student is a good problem solver



(3) If a student does well in
IST 230, then the student is a good problem solver



(4) If a student is a good
problem solver, then the student enjoys solving puzzles















2. Give the definition and a
concrete example of a proper subset






3. Let A be the set of all integers
x such that x is = k2 for some integer k



Let B be the set of all integers x such that the square
root of x, SQRT(x), is an integer



Give a formal proof that A = B. Remember
you must prove two things: (1) if x is in A, then x is in B, AND (2) if x is in B, then x is in A


















4. Explain when two sets are
disjoint and give a concrete example






Tell
whether or not the following are equal. Explain your answers. HINT: look
carefully at the notations used



5. {1, 2, 1, 3} = {3, 2, 1} 



6. (1, 2, 1, 3) = (3, 2, 1) 



7. (1, 2, 1, 3) = (1, 2, 3, 1) 








Let
 A = {5, 6} B = {g, h, i} C = {a, b}





8.
Calculate A
x B x C =


















Let A = {1, 2, x} B = {d, e, f} C = {2, x, y} U = {1, 2, d, e, f, x, y}





9.
Calculate A
? C =






10.
Calculate A
? B =






11.
Calculate A
– C =






12.
Calculate CC (the set complement of C) =






13. Give an example of a partition
of set U