Math 1090 A Homework 5 Math 1090 A Homework 5
Due December 1 at Noon.

  1. Fill in correct REASONS and complete the following to a proof that
    |-  (("x|:Ax) (Ay By)) By  .

    (("x|:Ax) (Ay By)) By
    =        REASONS        
    (("x|:Ax)true (Ay By)) By
    =        REASONS         
    (("x|:Ax)(("x |: Ax) Ay) (Ay By)) By

  2. Prove (8.18) where * is , i.e.,
    |-  ("x | R S : P) = ("x | R : P) ("x | S : P).

    Hint: Use (9.2), (3.78), (8.15) for " with R being ``true'', and finally (9.2) again.
    1. Prove
      |- ($|:true) = true .
    2. Prove
      |- ($|: P ("x |:P) ) .

  3. Prove
    |- ("x|:Ax)  ("x|:Bx)      ("x|:("x|:Ax)  Bx)
    and use to prove
    |- ("x|:Ax)  ("x|:Bx)      ("x|:("y|:Ay   Bx) ) .
  4. Prove without using (9.13),
    ("x|:P)     (" x|:P)   P[x: = a] .
    Hint: Use (8.17) and (8.14).


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On 18 Nov 2000, 17:30.