Print this problem set out (there 10 problems!) and answer the problems on the given sheet.

1. What is true ⊕ true? ___________________________
2. What is false ⇒ false?___________________________
3. draw a truth table for your own binary operator that is different from $\wedge,\vee,\Rightarrow,\Leftrightarrow$ and $\oplus$. Can you give a meaningful name to the operator?
4. Prove that (x1) ⊕ (¬((x2) ⊕ (x1))) is a propositional formula


5. Draw the expression tree for a⇒¬b∧a⇒c
6. Evaluate a⇒¬b∧a⇒c under the interpretation (a,b,c) = (true,false,true)
7. Evaluate a⇒¬b∧a⇒c under the interpretation (a,b,c) = (false,false,false)


8. Evaluate (a ⊕ c) ⇔ (¬c ∨ ¬b ) under the interpretation (a,b,c) = (false,true,false)
9. Find an interpretation under which (a⇒c) ⊕ (¬c ∨ ¬b ∨ a) evaluates to true
   [Extra Credit - don't look at it 'til you have your own answer to this problem ... it may mislead you!]
10. Draw the truth table for the boolean function g(a,b) defined by the propositional formula (a ⇒ b) ∧ ¬(¬a ⊕ b)
    ignore this, we didn't get quite far enough