Discrete Mathematics for Computer Science Mathematical Logic Questions

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Math Questions for Tutor
Instructions: Answer every question posted below with complete workout and steps where
possible
1.
The sequence S = (S0, S1, S2, S3, S4, S5, S6, . . . ), with base index 0, is recursively defined as
follows:
Initial Conditions: S0 = 1 and S1 = -3
Recurrence Relation: Sn = (Sn−1) + (6)( Sn−2) for each index n > 1.
Find the (integer) values of the following terms of S:
S2 =???
S3 =???
S4 =???
S5 =???
S6 =???
2.
Find the exact value
3.
Consider the following three-element set of symbols:
U = { u, v, w }
Provide a set-roster description of the power set of U.
4.
Consider the following two sets:
A = { 1, 4, 7, 10, 13, 16 } and B = { 3, 5, 7, 9, 11, 13, 15, 17 }
Provide a set-roster description of their intersection, A ∩ B.
5.
Consider the following two sets:
A = { 3, 5, 7, 9, 11, 13, 15, 17 } and B = { 3, 6, 9, 12, 15, 18 }
Provide a set-roster description of their union, A U B.
6.
Consider the following two sets:
A = { 4, 6, 8, 10, 12, 14, 16, 18 } and B = { 3, 6, 9, 12, 15, 18 }
Provide a set-roster description of their set difference, A − B.
7.
View the set A = { 2, 5, 8 } as a subset of the universal set U = { 1, 2, 3, 4, 5, 6, 7, 8, 9 }.
Provide a set-roster description of the complement of A ( i.e., Ac ).
8.
Consider the following two sets:
A = { 6, 7, 8 } and B = { 0, 2, 4 }
Provide a set-roster description of their Cartesian product, A × B.
9. Multiple Choice Question
Suppose that A, B, and D are subsets of a universal set U.
The expression
( [ A ∩ ( Ac U D ) ] ∩ B ) U ( Ac ∩ [ ( B U D c ) ∩ D ] )
must be equal to which of the following? (Choose only one answer.)
1.
2.
3.
4.
A∩B
U
BUD
B∩D
5. A U B

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sequence

discrete mathematics

logical math questions

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