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Q36E

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Found in: Page 36

### Discrete Mathematics and its Applications

Book edition 7th
Author(s) Kenneth H. Rosen
Pages 808 pages
ISBN 9780073383095

# Construct a truth table for each of these compound propositions.a) ${\mathbf{\left(}}{\mathbf{p}}{\mathbf{\vee }}{\mathbf{q}}{\mathbf{\right)}}{\mathbf{\vee }}{\mathbf{r}}$b) $\left(p\vee q\right){\mathbf{\wedge }}{\mathbf{r}}$c) $\left(p\wedge q\right){\mathbf{\vee }}{\mathbf{r}}$d) $\left(p\wedge q\right){\mathbf{\vee }}{\mathbf{r}}$e) $\left(p\vee q\right){\mathbf{\wedge }}{\mathbf{¬}}{\mathbf{r}}$f) $\left(p\wedge r\right){\mathbf{\vee }}{\mathbf{¬}}{\mathbf{r}}$

a)

 p q r $\mathrm{p}\vee \mathrm{q}$ $\left(\mathrm{p}\vee \mathrm{q}\right)\vee \mathrm{r}$ T T T T T T T F T T T F T T T T F F T T F T T T T F T F T T F F T F T F F F F F

b)

 p q r $\mathrm{p}\vee \mathrm{q}$ $\left(\mathrm{p}\wedge \mathrm{r}\right)\vee \mathrm{r}$ T T T T T T T F T F T F T T T T F F T F F T T T T F T F T F F F T F F F F F F F

c)

 p q r $\mathrm{p}\wedge \mathrm{q}$ $\left(\mathrm{p}\wedge \mathrm{q}\right)\vee \mathrm{r}$ T T T T T T T F T T T F T F T T F F F F F T T F T F T F F F F F T F T F F F F F

d)

 p q r $\mathrm{p}\wedge \mathrm{q}$ $\left(\mathrm{p}\wedge \mathrm{q}\right)\wedge \mathrm{r}$ T T T T T T T F T F T F T F F T F F F F F T T F F F T F F F F F T F F F F F F F

e)

 p q r $\mathrm{p}\vee \mathrm{q}$ $\left(\mathrm{p}\vee \mathrm{q}\right)\wedge ¬\mathrm{r}$ T T T T F T T F T T T F T T F T F F T T F T T T F F T F T T F F T F F F F F F F

f)

 p q r $\mathrm{p}\wedge \mathrm{q}$ $\left(\mathrm{p}\wedge \mathrm{q}\right)\vee ¬\mathrm{r}$ T T T T T T T F T T T F T F F T F F F T F T T F F F T F F T F F T F F F F F F T
See the step by step solution

## Definition of truth table

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

## Truth table for a)

The truth table for given statement is as follows,

 p q r $\mathrm{p}\vee \mathrm{q}$ $\left(\mathrm{p}\vee \mathrm{q}\right)\vee \mathrm{r}$ T T T T T T T F T T T F T T T T F F T T F T T T T F T F T T F F T F T F F F F F

## Truth table for b)

The truth table for given statement is as follows,

 p q r $\mathrm{p}\vee \mathrm{q}$ $\left(\mathrm{p}\vee \mathrm{q}\right)\wedge \mathrm{r}$ T T T T T T T F T F T F T T T T F F T F F T T T T F T F T F F F T F F F F F F F

## Truth table for c)

The truth table for given statement is as follows,

 p q r $\mathrm{p}\wedge \mathrm{q}$ $\left(\mathrm{p}\wedge \mathrm{q}\right)\vee \mathrm{r}$ T T T T T T T F T F T F T T T T F F T F F T T T T F T F T F F F T F F F F F F F

## Truth table for d)

The truth table for given statement is as follows,

 p q r $\mathrm{p}\wedge \mathrm{q}$ $\left(\mathrm{p}\wedge \mathrm{q}\right)\wedge \mathrm{r}$ T T T T T T T F T F T F T F F T F F F F F T T F F F T F F F F F T F F F F F F F

## Truth table for e)

The truth table for given statement is as follows,

 p q r $\mathrm{p}\vee \mathrm{q}$ $\left(\mathrm{p}\vee \mathrm{q}\right)¬\mathrm{r}$ T T T T F T T F T T T F T T F T F F T T F T T T F F T F T T F F T F F F F F F F

## Truth table for f)

The truth table for given statement is as follows,

 p q r $\mathrm{p}\wedge \mathrm{q}$ $\left(\mathrm{p}\wedge \mathrm{q}\right)\vee ¬\mathrm{r}$ T T T T T T T F T T T F T F F T F F F T F T T F F F T F F T F F T F F F F F F T