c-cl-selo(1)

# c-cl-selo(1) - C2 Give an explicit bijection f C → H...

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Sets and Logic MHF3202 4628 Class-C Prof. JLF King 07Feb2008 C1: Show no work. Write DNE ( for “ Does Not Exist ) in a blank if the indicated operation cannot be per- formed, or if the described object does not exist. Use V () for the Vince invariant of a cell in a TicTacToe board. Use TTT to abbreviate “TicTacToe”. a The author of our text is ± ² ³ ´ Circle : Archimedes Cantor DNE Euler Devlin Machen b In Qubic , V ( Center cell )= ....... . And V ( Edge cell )= ....... . There are ....... many cells whose Vince-invariant equals V ( Edge cell ). c The 7 × 7 TTT board has .... many TicTacToes. And 4 × 4 × 4 ( Qubic ) has .......... many TicTacToes. d An explicit bijection f : N , ± Z is If n is even , then f ( n ) := .......................... . If n is odd , then f ( n ) := ........................... . e An explicit bijection g : ( π 2 , π 2 ) , ± R is g ( x ) := ........................................... . f LBolt: Gcd(70 , 42)= ....... · 70 + ....... · 42. So (use LBolt twice) G := Gcd(70 , 42 , 30)= ...... and ........ · 70 + ........ · 42 + ........ · 30 = G . Essay questions: For each question, carefully write a triple– spaced, grammatical, essay solving the problem.
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Unformatted text preview: C2: Give an explicit bijection f : C → H between inter-vals C := ( , 4 ] and H := ( , 4 ) . C3: α The powerset P (Ω) of set Ω , is ... . β Give a complete proof that there is no sur-jection h : Ω ± P (Ω). In particular, given a map h : Ω ± P (Ω), explicitly construct a set S h ⊂ Ω which is guaranteed to not be in the range of h . γ When Ω := { M,L,C } , the three Stooges, consider this map g ( M ) := { M,L,C } ; g ( L ) := { M,C } ; g ( C ) := {} . Your S g = { ............... } . End of Class-C C1: 150pts C2: 65pts C3: 80pts Total: 295pts Print name ............................................... Ord: Honor Code: “I have neither requested nor received help on this exam other than from my professor (or his col-league) .” Signature: .............................................
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