#### Symbolic Logic

1. ((A ∧ B) ∨ C)

2. ((~ D ∧ ~ E) ∨ ~ F)

3. ~ (~ (G ∧ H) ∨ I)

4. ~ (~ (~ J ∧ ~ K) ∨ ~ L)

5. (M → N) ↔ (P → Q)

6. (((~ R ∧ S) ∧ ~ T) ∧ U)

7. (W ∧ (~ X ∧ (Y ∧ ~ Z)))

8. ((~ A ∨ ~ B) ∧ ~ (C ∨ D)) → ~ E

9. ~ F ∨ ((~ G ∧ ~ H) ∨ (I → ~ J)) 10. (~ ~ ~ ~ ~ K ∧ ~ ~ ~ ~ L) ∨ ~ ~ ~ M

2. For each of the following arguments, provide an interpretation that shows the argument to be invalid.

3. For each of the following sets of statements, provide an interpretation that shows the statements to be consistent-i.e. can all be satisfied in the same interpretation.

Easier statement: For all y = Q there exists r = Z such that (y<r or r < y + 5) or r³ +3 ≤ y. Harder statement: For all y = Q there exists r € Z such that (y<r or r < y + 5) only if r³ +3 ≤ 7. 1. You will be given two logical statements, one easier and one harder. 2. Choose one of the two statements. 3. Write out the logical statement. 4. Write it out again using logical symbols (and 33, and arrows for the harder statement). 5. Write out the negation of the statement in words and in symbols. 6. State which of the two statements (the original one or it's negation) is true. 7. Give a well-written proof.

Construct a complete truth table for the following SL sentence, determine whether or not it is truth- functionally true, truth-functionally false, or truth-functionally indeterminate, and briefly state why.

Construct a complete truth table for the following SL sentence, determine whether or not it is truth- functionally true, truth-functionally false, or truth-functionally indeterminate, and briefly state why.

Construct a complete truth table for the following SL sentence, determine whether or not it is truth- functionally true, truth-functionally false, or truth-functionally indeterminate, and briefly state why. (X=0) & (X= ~O)