1)In Set Theory the difference of two sets, A and B is defined as: A 1)In Set Th
ID: 3570491 • Letter: 1
Question
1)In Set Theory the difference of two sets, A and B is defined as:
A
1)In Set Theory the difference of two sets, A and B is defined as: A ?? B = { s | s belongs to A and s does not belong to B } Define the difference of two sets A and B, using only the basic operations of set theory: union, intersection, and complement. A ?? B = ___________________ 2)In terms of an Abstract Boolean algebra, for two elements x and y define the difference, x ?? y using the basic operations +, ?, and ~ of Boolean algebra, using the definition from Set Theory as your guide. x ?? y ______________ 3) In Boolean algebra rewrite the expression x ?? (y + z) using only the basics operations of ~ , ? and +. x ?? ( y + z ) = _______________________ 4) Using the results of Boolean algebra in problem 13 above, rewrite the set theoretic expression of A ?? ( B U C ) = ___________________________ 5) Consider two sets A and B. Define a set C, which consists only of those elements, which are either in A and not in B or in B and not in A. So C = { s | s belongs to A and s does not belong to B or s belongs to B and s does not belong to A } Define the set C using only the basic operations of set theory: union, intersection, and complement. C = _______________________ U C ) using only the basics operations of set theory: union, intersection, and complement. A ?? ( BExplanation / Answer
A = {1, 4, 6, 3, 8} B = {3, 5, 6, 9, 7} C={3, 7, 5}
1)
A-B = {1, 4, 8}
2)
x = {1, 4, 6, 3, 8} y= {3, 5, 6, 9, 7} Z={3, 7, 5}
X - Y = {1, 4 , 8}
3)
x
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