Chapter 1.1, Problem 57E

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6th Edition

Daniel C. Alexander + 1 other

ISBN: 9781285195698

Textbook Problem

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*In Exercises 55 and 56, P is a true statement, while Q and R are false statements. Classify each of the following statements as true or false.*

a)

b)

To determine

**a)**

**To classify:**

Each statement as true or false.

Explanation

**Approach:**

Conjunction:

In logic, a conjunction is a compound sentence formed by using the word ** and** to join two simple sentences.

If* P* and *Q* are letters used to represent simple statements, then a statement of the form “*P* and *Q*” is known as a conjunction of statement *P* and statement *Q*.

The truth of a conjunction is given by:

P |
Q |
P and Q |

T | T | T |

T | F | F |

F | T | F |

F | F | F |

In the above table, T = True, F = False.

Thus, a conjunction is true only when both *P* and *Q* are true.

Disjunction:

In logic, disjunctions are compound sentences made up of two or more simple sentences connected with “or”.

If *P* and *Q* are letters used to represent simple statements, then a statement of the form “*P* or *Q*” is known as a disjunction of statement *P* and statement *Q*.

The truth of a disjunction is given by:

P |
Q |
P and Q |

T | T | T |

T | F | T |

F | T | T |

F | F | F |

In the above table, T = True, F = False.

Thus, a disjunction is true when either of the statements is true. A disjunction is false only when both the statements are false.

Negation of a statement:

The negation of a given statement *P* makes a claim opposite that of the original statement. If the given statement is true, its negation is false, and vice versa. If *P* is a statement, we use *P*”) to indicate its negation.

**Procedure:**

The given statement is:

The truth value of each statement is as follows:

Statement | Truth Value |

P | T |

Q | F |

R | F |

First, let’s evaluate the bracket

To determine

**b)**

**To classify:**

Each statement as true or false.

Sect-1.1 P-1ESect-1.1 P-2ESect-1.1 P-3ESect-1.1 P-4ESect-1.1 P-5ESect-1.1 P-6ESect-1.1 P-7ESect-1.1 P-8ESect-1.1 P-9ESect-1.1 P-10E

Sect-1.1 P-11ESect-1.1 P-12ESect-1.1 P-13ESect-1.1 P-14ESect-1.1 P-15ESect-1.1 P-16ESect-1.1 P-17ESect-1.1 P-18ESect-1.1 P-19ESect-1.1 P-20ESect-1.1 P-21ESect-1.1 P-22ESect-1.1 P-23ESect-1.1 P-24ESect-1.1 P-25ESect-1.1 P-26ESect-1.1 P-27ESect-1.1 P-28ESect-1.1 P-29ESect-1.1 P-30ESect-1.1 P-31ESect-1.1 P-32ESect-1.1 P-33ESect-1.1 P-34ESect-1.1 P-35ESect-1.1 P-36ESect-1.1 P-37ESect-1.1 P-38ESect-1.1 P-39ESect-1.1 P-40ESect-1.1 P-41ESect-1.1 P-42ESect-1.1 P-43ESect-1.1 P-44ESect-1.1 P-45ESect-1.1 P-46ESect-1.1 P-47ESect-1.1 P-48ESect-1.1 P-49ESect-1.1 P-50ESect-1.1 P-51ESect-1.1 P-52ESect-1.1 P-53ESect-1.1 P-54ESect-1.1 P-55ESect-1.1 P-56ESect-1.1 P-57ESect-1.2 P-1ESect-1.2 P-2ESect-1.2 P-3ESect-1.2 P-4ESect-1.2 P-5ESect-1.2 P-6ESect-1.2 P-7ESect-1.2 P-8ESect-1.2 P-9ESect-1.2 P-10ESect-1.2 P-11ESect-1.2 P-12ESect-1.2 P-13ESect-1.2 P-14ESect-1.2 P-15ESect-1.2 P-16ESect-1.2 P-17ESect-1.2 P-18ESect-1.2 P-19ESect-1.2 P-20ESect-1.2 P-21ESect-1.2 P-22ESect-1.2 P-23ESect-1.2 P-24ESect-1.2 P-25ESect-1.2 P-26ESect-1.2 P-27ESect-1.2 P-28ESect-1.2 P-29ESect-1.2 P-30ESect-1.2 P-31ESect-1.2 P-32ESect-1.2 P-33ESect-1.2 P-34ESect-1.2 P-35ESect-1.2 P-36ESect-1.2 P-37ESect-1.2 P-38ESect-1.2 P-39ESect-1.2 P-40ESect-1.2 P-41ESect-1.2 P-42ESect-1.2 P-43ESect-1.2 P-44ESect-1.2 P-45ESect-1.2 P-46ESect-1.2 P-47ESect-1.2 P-48ESect-1.2 P-49ESect-1.2 P-50ESect-1.3 P-1ESect-1.3 P-2ESect-1.3 P-3ESect-1.3 P-4ESect-1.3 P-5ESect-1.3 P-6ESect-1.3 P-7ESect-1.3 P-8ESect-1.3 P-9ESect-1.3 P-10ESect-1.3 P-11ESect-1.3 P-12ESect-1.3 P-13ESect-1.3 P-14ESect-1.3 P-15ESect-1.3 P-16ESect-1.3 P-17ESect-1.3 P-18ESect-1.3 P-19ESect-1.3 P-20ESect-1.3 P-21ESect-1.3 P-22ESect-1.3 P-23ESect-1.3 P-24ESect-1.3 P-25ESect-1.3 P-26ESect-1.3 P-27ESect-1.3 P-28ESect-1.3 P-29ESect-1.3 P-30ESect-1.3 P-31ESect-1.3 P-32ESect-1.3 P-33ESect-1.3 P-34ESect-1.3 P-35ESect-1.3 P-36ESect-1.3 P-37ESect-1.3 P-38ESect-1.3 P-39ESect-1.3 P-40ESect-1.3 P-41ESect-1.4 P-1ESect-1.4 P-2ESect-1.4 P-3ESect-1.4 P-4ESect-1.4 P-5ESect-1.4 P-6ESect-1.4 P-7ESect-1.4 P-8ESect-1.4 P-9ESect-1.4 P-10ESect-1.4 P-11ESect-1.4 P-12ESect-1.4 P-13ESect-1.4 P-14ESect-1.4 P-15ESect-1.4 P-16ESect-1.4 P-17ESect-1.4 P-18ESect-1.4 P-19ESect-1.4 P-20ESect-1.4 P-21ESect-1.4 P-22ESect-1.4 P-23ESect-1.4 P-24ESect-1.4 P-25ESect-1.4 P-26ESect-1.4 P-27ESect-1.4 P-28ESect-1.4 P-29ESect-1.4 P-30ESect-1.4 P-31ESect-1.4 P-32ESect-1.4 P-33ESect-1.4 P-34ESect-1.4 P-35ESect-1.4 P-36ESect-1.4 P-37ESect-1.4 P-38ESect-1.4 P-39ESect-1.4 P-40ESect-1.4 P-41ESect-1.4 P-42ESect-1.4 P-43ESect-1.4 P-44ESect-1.4 P-45ESect-1.4 P-46ESect-1.5 P-1ESect-1.5 P-2ESect-1.5 P-3ESect-1.5 P-4ESect-1.5 P-5ESect-1.5 P-6ESect-1.5 P-7ESect-1.5 P-8ESect-1.5 P-9ESect-1.5 P-10ESect-1.5 P-11ESect-1.5 P-12ESect-1.5 P-13ESect-1.5 P-14ESect-1.5 P-15ESect-1.5 P-16ESect-1.5 P-17ESect-1.5 P-18ESect-1.5 P-19ESect-1.5 P-20ESect-1.5 P-21ESect-1.5 P-22ESect-1.5 P-23ESect-1.5 P-24ESect-1.5 P-25ESect-1.5 P-26ESect-1.5 P-27ESect-1.5 P-28ESect-1.5 P-29ESect-1.5 P-30ESect-1.5 P-31ESect-1.5 P-32ESect-1.5 P-33ESect-1.5 P-34ESect-1.5 P-35ESect-1.5 P-36ESect-1.5 P-37ESect-1.5 P-38ESect-1.6 P-1ESect-1.6 P-2ESect-1.6 P-3ESect-1.6 P-4ESect-1.6 P-5ESect-1.6 P-6ESect-1.6 P-7ESect-1.6 P-8ESect-1.6 P-9ESect-1.6 P-10ESect-1.6 P-11ESect-1.6 P-12ESect-1.6 P-13ESect-1.6 P-14ESect-1.6 P-15ESect-1.6 P-16ESect-1.6 P-17ESect-1.6 P-18ESect-1.6 P-19ESect-1.6 P-20ESect-1.6 P-21ESect-1.6 P-22ESect-1.6 P-23ESect-1.6 P-24ESect-1.6 P-25ESect-1.6 P-26ESect-1.6 P-27ESect-1.6 P-28ESect-1.6 P-29ESect-1.6 P-30ESect-1.7 P-1ESect-1.7 P-2ESect-1.7 P-3ESect-1.7 P-4ESect-1.7 P-5ESect-1.7 P-6ESect-1.7 P-7ESect-1.7 P-8ESect-1.7 P-9ESect-1.7 P-10ESect-1.7 P-11ESect-1.7 P-12ESect-1.7 P-13ESect-1.7 P-14ESect-1.7 P-15ESect-1.7 P-16ESect-1.7 P-17ESect-1.7 P-18ESect-1.7 P-19ESect-1.7 P-20ESect-1.7 P-21ESect-1.7 P-22ESect-1.7 P-23ESect-1.7 P-24ESect-1.7 P-25ESect-1.7 P-26ESect-1.7 P-27ESect-1.7 P-28ESect-1.7 P-29ESect-1.7 P-30ESect-1.7 P-31ESect-1.7 P-32ESect-1.7 P-33ESect-1.7 P-34ESect-1.7 P-35ESect-1.CR P-1CRSect-1.CR P-2CRSect-1.CR P-3CRSect-1.CR P-4CRSect-1.CR P-5CRSect-1.CR P-6CRSect-1.CR P-7CRSect-1.CR P-8CRSect-1.CR P-9CRSect-1.CR P-10CRSect-1.CR P-11CRSect-1.CR P-12CRSect-1.CR P-13CRSect-1.CR P-14CRSect-1.CR P-15CRSect-1.CR P-16CRSect-1.CR P-17CRSect-1.CR P-18CRSect-1.CR P-19CRSect-1.CR P-20CRSect-1.CR P-21CRSect-1.CR P-22CRSect-1.CR P-23CRSect-1.CR P-24CRSect-1.CR P-25CRSect-1.CR P-26CRSect-1.CR P-27CRSect-1.CR P-28CRSect-1.CR P-29CRSect-1.CR P-30CRSect-1.CR P-31CRSect-1.CR P-32CRSect-1.CR P-33CRSect-1.CR P-34CRSect-1.CR P-35CRSect-1.CR P-36CRSect-1.CR P-37CRSect-1.CR P-38CRSect-1.CR P-39CRSect-1.CR P-40CRSect-1.CR P-41CRSect-1.CR P-42CRSect-1.CR P-43CRSect-1.CR P-44CRSect-1.CR P-45CRSect-1.CR P-46CRSect-1.CR P-47CRSect-1.CR P-48CRSect-1.CR P-49CRSect-1.CR P-50CRSect-1.CR P-51CRSect-1.CR P-52CRSect-1.CT P-1CTSect-1.CT P-2CTSect-1.CT P-3CTSect-1.CT P-4CTSect-1.CT P-5CTSect-1.CT P-6CTSect-1.CT P-7CTSect-1.CT P-8CTSect-1.CT P-9CTSect-1.CT P-10CTSect-1.CT P-11CTSect-1.CT P-12CTSect-1.CT P-13CTSect-1.CT P-14CTSect-1.CT P-15CTSect-1.CT P-16CTSect-1.CT P-17CTSect-1.CT P-18CTSect-1.CT P-19CTSect-1.CT P-20CTSect-1.CT P-21CTSect-1.CT P-22CTSect-1.CT P-23CT

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