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Chapter 3: Problem 89

Under which conditions is a disjunction true?

Short Answer

Expert verified
A disjunction is true when both its components are true, when the first component is true and the second isn't, or when the first component isn't true but the second is. It is only false when both components are false.

Step by step solution

01

Understanding Disjunction

A disjunction in logic is usually consists of two statements linked by the word 'or'. The disjunction itself is symbolized as P 鈭� Q, where P and Q are the individual statements.
02

True Disjunction 1

The first condition for a disjunction to be true is when both the connected statements are true. If P is true and Q is also true, then the combined statement (P 鈭� Q) will be true.
03

True Disjunction 2

The second condition is when the first part is true, but the second part is not. If P is true and Q is false, then the combined statement (P 鈭� Q) is still true.
04

True Disjunction 3

The third condition is when the first part is not true, but the second part is. If P is false and Q is true, then the combined statement (P 鈭� Q) is also true.
05

False Disjunction

The only time a disjunction is false is when both components are false. If P is false and Q is also false, then the combined statement (P 鈭� Q) will be false.

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Most popular questions from this chapter

Use a truth table to determine whether the symbolic form of the argument is valid or invalid. $$ \begin{aligned} &p \rightarrow q \\ &\frac{q \rightarrow p}{\therefore p \wedge q} \end{aligned} $$

Write an original argument in words for the contrapositive reasoning form.

Use Euler diagrams to determine whether each argument is valid or invalid. All comedians are funny people. Some comedians are professors. Therefore, some funny people are professors.

Translate each argument into symbolic form. Then determine whether the argument is valid or invalid. You may use a truth table or, if applicable, compare the argument's symbolic form to a standard valid or invalid form. (You can ignore differences in past, present, and future tense.) If it rains or snows, then I read. I am not reading. \(\therefore\) It is neither raining nor snowing.

Use Euler diagrams to determine whether each argument is valid or invalid. All dancers are athletes. Savion Glover is a dancer. Therefore, Savion Glover is an athlete.
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