Use Indirect Truth Tables to Determine, for Each Given Set $\lor$

question 128

Multiple Choice

use indirect truth tables to determine, for each given set of propositions, whether it is consistent. If the set is consistent, choose an option with a consistent valuation. (There may be other consistent valuations.)
-D ≡ (A • B)
D $\lor$ (∼E • F)
∼E ⊃ A
F ⊃ B
A $\lor$ B
∼A $\lor$ ∼B

• A) Inconsistent
• B) Consistent. Consistent valuation when A and F are true and B, D, and E are false
• C) Consistent. Consistent valuation when A, D, and E are true and B and F are false
• D) Consistent. Consistent valuation when B, D, and E are true and A and F are false
• E) Consistent. Consistent valuation when B and F are true and A, D, and E are false

---

Definitions:

Leaf

In the context of a tree data structure, a leaf is a node that has no children.

Stem

In the context of data visualization, the stem represents the main part of a stem-and-leaf plot, displaying digits for significant value while the leaf displays less significant digits.

Split the Stems

A technique used in stem-and-leaf plots to spread out the data more evenly across the plot by splitting the stems to create more intervals.

Stemplot

A graphical method used in statistics to display the distribution of a dataset, where each number is split into a stem and a leaf, thus showing the shape of the data.