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Q29

Expert-verifiedFound in: Page 15

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) ${\mathbf{(}}{\mathit{p}}{\mathbf{\vee}}{\mathbf{\neg}}{\mathit{r}}{\mathbf{)}}{\mathbf{\wedge}}{\mathbf{(}}{\mathit{q}}{\mathbf{\vee}}{\mathbf{\neg}}{\mathit{s}}{\mathbf{)}}$**

**c) ${\mathit{q}}{\mathbf{\vee}}{\mathit{p}}{\mathbf{\vee}}{\mathbf{\neg}}{\mathit{s}}{\mathbf{\vee}}{\mathbf{\neg}}{\mathit{r}}{\mathbf{\vee}}{\mathbf{\neg}}{\mathit{t}}{\mathbf{\vee}}{\mathit{u}}$**

**d) \((p \wedge r \wedge t) \leftrightarrow (q \wedge t)\)**

a) 2 rows

b) 16 rows

c)** 64 **rows

d) 16 rows

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

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

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

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

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

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

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

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

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

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