3.2 E / 1a, c, f; 2a – f (Truth, Falsity, Indeterminacy)
3.3 E / 1b, e, k; 2a – f (Equivalence and Nonequivalence)
3.4 E / 1d, e, f; 2a – f (Consistency and Inconsistency)
3.5 E / 1e, f, h; 2a – e (Validity and Invalidity)
3.2E
EXERCISES
1. Construct a full truth-table for each of the following sentences of SL, and
state whether the sentence is truth-functionally true, truth-functionally false,
or truth-functionally indeterminate.
a. ∼ A ⊃ A
c. (A ! ∼ A) ⊃ ∼ (A ! ∼ A)
*f. ([(C ⊃ D) & (D ⊃ E)] & C) & ∼ E
2. For each of the following sentences, either show that the sentence is truth-
functionally true by constructing a full truth-table or show that the sentence
is not truth-functionally true by constructing an appropriate shortened
truth-table.
a. (F ∨ H) ∨ (∼ F ! H) *d. A ! (B ! A)
*f. [C ⊃ (C ∨ ∼ D)] ⊃ (C ∨ D)
3.3E EXERCISES
1. Determine, by constructing full truth-tables, which of the following pairs of
sentences of SL are truth-functionally equivalent.
*b. A ⊃ (B ⊃ A) (C & ~ C) ∨ (A ⊃ A)
e. (G ⊃ F) ⊃ (F ⊃ G) (G ! F) ∨ (~ F ∨ G)
k. F ∨ ~ (G ∨ ~ H) (H ! ~ F) ∨ G
2. For each of the following pairs of sentences of SL, either show that the sen-
tences are truth-functionally equivalent by constructing a full truth-table or
show that they are not truth-functionally equivalent by constructing an appro-
priate shortened truth-table.
a. G ∨ H. ∼ G ⊃ H
*f. ∼ (∼ B ∨ (∼ C ∨ ∼ D)) (D ∨ C) & ∼ B
3.4E EXERCISES
1. Construct full truth-tables for each of the following sets of sentences and
indicate whether they are truth-functionally consistent or truth-functionally
*d. {(A & B) & C, C ∨ (B ∨ A), A ! (B ⊃ C)}
e. {( J ⊃ J) ⊃ H, ∼ J, ∼ H}
*f. {U ∨ (W & H), W ! (U ∨ H), H ∨ ∼ H}
2. For each of the following sets of sentences, either show that the set is truth-
functionally consistent by constructing an appropriate shortened truth-table or
show that the set is truth-functionally inconsistent by constructing a full truth-
table.
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