1.
a. A set of sentences of SL is truth-functionally consistent if and only if there is at
least one truth-value assignment on which all of the members of the set are
true.
b. A sentence P of SL is truth-functionally true if and only if P is true on every
truth-value assignment.
2.
P ~P P Q P v Q P & Q P ⊃ Q P ≡ Q
T F T T T T T T
F T T F T F F F
F T T F T F
F F F F T T
~ rule : A negation, ~P, receives the opposite truth value of its immediate
component, P.
v rule: A disjunction, P v Q, is true if and only if at least one of P or Q is true;
otherwise it is false.
& rule: A conjunction, P & Q, is true if and only if both P and Q are true;
otherwise it is false.
⊃ rule: A conditional, P ⊃ Q, is true if and only if either its antecedent, P, is false
or it consequent, Q, is true; otherwise it is false.
≡ rule: A biconditional, P ≡ Q, is true if and only if P and Q have the same truth
value; otherwise it is false.
3. a. F
b. F
c. T
d. F
e. F
4.
a. Truth-functionally indeterminate because there is at least one line (truth value
assignment) that assigns T to the main connective and at least one that
assigns F.
↓
F H J ~ [F & (H ≡ J)] (~ H v J)
⊃
T T T F T T T T T T F T T T
T T F T T F T F F F F T F F
T F T T T F F F T T T F T T
T F F F T T F T F T T F T F
F T T T F F T T T T F T T T
F T F T F F T F F F F T F F
F F T T F F F F T T T F T T
F F F T F F F T F T T F T F b. Truth-functionally valid because on every line (truth value assignment) either
at least one premise is false or the conclusion is true
↓ ↓ ↓
A C H ~ A ⊃ (C ≡ A) (H v A) ≡ C ~ C ⊃ (A ⊃ H)
T T T F T T T T T T T T T T F T T T T T
T T F F T T T T T F T T T T F T T T F F
T F T F T T F F T T T T F F T F T T T T
T F F F T T F F T F T T F F T F F T F F
F T T T F F T F F T T F T T F T T F T T
F T F T F F T F F F F F F T F T T F T F
F F T T F T F T F T T F F F T F T F T T
F F F T F T F T F F F F T F T F T F T F
5. a. Truth functional indeterminacy. You need to do two short truth tables, one that
starts off with the assignment of T to the main connective and one that starts off with the
assignment of F to the main connective.
b. Truth functional non-equivalence. You start off by making the assignment of a T to
the main connective of one of the sentences and an F to the main connective of the
other. As long as that works you are done. However, if contradictions prevent you from
arriving at a truth value assignment to the atomic components, you must try a second
truth table that reverses these assignments and gives an F to the main connective of
the sentence you made true on your first attempt, and a T to the main connective of the
one you made false.
c. Truth functional invalidity. You start off by making the assignment of a T to the main
connective of each premise and an F to the main connective of the conclusi

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