• :00Days
• :00Hours
• :00Mins
• 00Seconds
A new era for learning is coming soon

Suggested languages for you:

Americas

Europe

Q34E

Expert-verified
Found in: Page 35

### Discrete Mathematics and its Applications

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

# Find the dual of each of these compound propositions.a) $p\vee ¬q$b) ${p}{\wedge }{\left(}{q}{\vee }{\left(}{r}{\wedge }{T}{\right)}{\right)}$c) ${\left(}{p}{\wedge }{¬}{q}{\right)}{\vee }{\left(}{q}{\wedge }{F}{\right)}$

a) ${p}{\wedge }{¬}{q}$

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

c) ${\left(}{p}{\vee }{¬}{q}{\right)}{\wedge }{\left(}{q}{\vee }{T}{\right)}$

See the step by step solution

## Step1:Definition of dual

The dual of a proposition which contains only the logical operators $\vee ,\wedge ,¬$, is the compound proposition obtained by replacing each $\wedge$ by $\vee$ , each $\vee$ by $\wedge$ , each T by F, and each F by T.

## Step 2: Dual of a)

Dual of ${p}{\vee }{¬}{q}$ is ${p}{\wedge }{¬}{q}$

## Step 2: Dual of b)

Dual of ${p}{\wedge }{\left(}{q}{\vee }{\left(}{r}{\wedge }{T}{\right)}{\right)}$ is .${p}{\vee }{\left(}{q}{\wedge }{\left(}{r}{\vee }{F}{\right)}{\right)}$

## Step 3: Dual of c)

Dual of ${\left(}{p}{\wedge }{¬}{q}{\right)}{\vee }{\left(}{q}{\wedge }{F}{\right)}$ is ${\left(}{p}{\vee }{¬}{q}{\right)}{\wedge }{\left(}{q}{\vee }{T}{\right)}$${\left(}{p}{\vee }{¬}{q}{\right)}{\wedge }{\left(}{q}{\vee }{T}{\right)}$