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Expert-verified Found in: Page 15 ### Discrete Mathematics and its Applications

Book edition 7th
Author(s) Kenneth H. Rosen
Pages 808 pages
ISBN 9780073383095 # How many rows appear in a truth table for each of these compound propositions? a) $$p \to \neg p$$b) ${\mathbf{\left(}}{\mathbit{p}}{\mathbf{\vee }}{\mathbf{¬}}{\mathbit{r}}{\mathbf{\right)}}{\mathbf{\wedge }}{\mathbf{\left(}}{\mathbit{q}}{\mathbf{\vee }}{\mathbf{¬}}{\mathbit{s}}{\mathbf{\right)}}$c) ${\mathbit{q}}{\mathbf{\vee }}{\mathbit{p}}{\mathbf{\vee }}{\mathbf{¬}}{\mathbit{s}}{\mathbf{\vee }}{\mathbf{¬}}{\mathbit{r}}{\mathbf{\vee }}{\mathbf{¬}}{\mathbit{t}}{\mathbf{\vee }}{\mathbit{u}}$d) $$(p \wedge r \wedge t) \leftrightarrow (q \wedge t)$$

a) 2 rows

b) 16 rows

c) 64 rows

d) 16 rows

See the step by step solution

## Definition of truth table

A truth table is a mathematical table which is used in logic

## Rows in a)

The given statement $p\to ¬p$ has only one variable.

Hence, there are ${2}^{1}=2$ rows.

## Rows in b)

The given statement $\left(p\vee ¬r\right)\wedge \left(q\vee ¬s\right)$has variables.

Hence, there are ${2}^{4}=16$rows.

## Rows in c)

The given statement has $q\vee p\vee ¬s\vee ¬r\vee ¬t\vee u$variables.

Hence, there are ${2}^{6}=64$ rows

## Rows in d)

The given statement $$p \wedge r \wedge t) \leftrightarrow (q \wedge t)$$ has 4 variables.

Hence, there are ${2}^{4}=16$rows. ### Want to see more solutions like these? 