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Q34E

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)** $p\vee \neg q$

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

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

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

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

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

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 $\vee $ by $\wedge $ , each T by F, and each F by T.

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

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

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

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