Symbolic Logic Worksheet 3 Key
1. Complete the truth table below using your knowledge of symbolic logic.
p q ~q p ∧q p ∨q p →q q →p p ↔q p →~q p ∨q →p p ∧q →q
T T F T T T T T F T T
T F T F T F T F T T T
F T F F T T F F T F T
F F T F F T T T T T T
Answer questions 2 through 9 based on the truth table above.
2. Which statement is a negation? ~q
3. Which statements are conditionals? p →q, q →p, p →~q, p ∨q →p, p ∧q →q
4. Which statement is a disjunction? p ∨q
5. Which statement is a biconditional? p ↔q
6. Which statement is a conjunction? p ∧q
7. Which statements are logically equivalent? q →p and p ∨q →p
8. Which statement is a tautology? p ∧q →q
9. Determine which of the following statements are tautologies by constructing a truth table. Write yes or
no in the space provided.
a) r ∨~r yes
b) r →~r no
c) (x ∨y) →(x ∧y) no
d) ~(p ∨q) ↔(~p ∧~q) yes
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