Why did you choose the method? How did you apply problem-solving in your proof?

Answer those for my answer:

9. Show that the following statements are equivalent by writing each in logical symbols (using ,, etc.) and then showing that the resulting formulas are equivalent. a. A B and A B = B b. A B and A B = A

Showing that the statements are

a. A B and A B = B

• Assume that A B
• If xAB, thenxAorxB.
  • ThereforeABB.
• IfxBthenxAB.
  • ThereforeBAB
• A B iff A B = B.

b. A B and A B = A

• Assume that A B
  • IfxAB,it must bexAand xB
    • ThereforeABA
• Show that AAB
  • ifxA,xBthen xAB
    • AAB
    • ThereforeAB=A
• AB=A
  • If aA, then aaAB
  • Also,aB,thenAB
• A B iff A B = A