Book edition 7th

Author(s) Kenneth H. Rosen

Pages 808 pages

ISBN 9780073383095

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Short Answer

How many rows appear in a truth table for each of these compound propositions?
a) $p \to \neg p$
b) $(p \lor \neg r) \land (q \lor \neg s)$
c) $q \lor p \lor \neg s \lor \neg r \lor \neg t \lor u$
d) $(p \wedge r \wedge t) \leftrightarrow (q \wedge t)$

a) 2 rows

b) 16 rows

c) 64 rows

d) 16 rows

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Definition of truth table

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

Rows in a)

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

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

Rows in b)

The given statement $(p \lor \neg r) \land (q \lor \neg s)$ has variables.

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

Rows in c)

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

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

Rows in d)

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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Discrete Mathematics and its Applications

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Short Answer

How many rows appear in a truth table for each of these compound propositions?
a) \(p \to \neg p\)
b) $(p \lor \neg r) \land (q \lor \neg s)$
c) $q \lor p \lor \neg s \lor \neg r \lor \neg t \lor u$
d) \((p \wedge r \wedge t) \leftrightarrow (q \wedge t)\)

Step by Step Solution

Definition of truth table

Rows in a)

Rows in b)

Rows in c)

Rows in d)

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How many rows appear in a truth table for each of these compound propositions? a) \(p \to \neg p\)b) (p∨¬r)∧(q∨¬s)c) q∨p∨¬s∨¬r∨¬t∨ud) \((p \wedge r \wedge t) \leftrightarrow (q \wedge t)\)

Step by Step Solution

Definition of truth table

Rows in a)

Rows in b)

Rows in c)

Rows in d)

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How many rows appear in a truth table for each of these compound propositions?
a) \(p \to \neg p\)
b) $(p \lor \neg r) \land (q \lor \neg s)$
c) $q \lor p \lor \neg s \lor \neg r \lor \neg t \lor u$
d) \((p \wedge r \wedge t) \leftrightarrow (q \wedge t)\)