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Q35E

Expert-verifiedFound in: Page 35

Book edition
7th

Author(s)
Kenneth H. Rosen

Pages
808 pages

ISBN
9780073383095

**Find the dual of each of these compound propositions..**

**a)** ${p}{\wedge}{\neg}{q}{\wedge}{\neg}{r}$

**b)** ${(}{p}{\wedge}{q}{\wedge}{r}{)}{\wedge}{s}$

**c) ${(}{p}{\vee}{F}{)}{\wedge}{(}{q}{\vee}{T}{)}$**

a) ${p}{\vee}{\neg}{q}{\vee}{\neg}{r}$

b) ${(}{p}{\vee}{q}{\vee}{r}{)}{\vee}{s}$

c) ${(}{p}{\wedge}{T}{)}{\vee}{(}{q}{\wedge}{F}{)}$

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

Dual of ${p}{\wedge}{\neg}{q}{\wedge}{\neg}{r}$ is . ${p}{\vee}{\neg}{q}{\vee}{\neg}{r}$

Dual of ${(}{p}{\wedge}{q}{\wedge}{r}{)}{\wedge}{s}$ is ${(}{p}{\vee}{q}{\vee}{r}{)}{\vee}{s}$

**Dual of ${(}{p}{\vee}{F}{)}{\wedge}{(}{q}{\vee}{T}{)}$ is ${(}{p}{\wedge}{T}{)}{\vee}{(}{q}{\wedge}{F}{)}$**

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