QuestionGiven statements $p$ : It is Friday, $q$ : There are students in the library. Fill in symbolic forms for (a) and (b), and descriptive for (c).

Studdy Solution

STEP 1

Assumptions1. $p$ represents the statement "It is Friday." . $q$ represents the statement "There are students in the library."
3. The symbol $\sim$ represents negation (not).
4. The symbol $\wedge$ represents conjunction (and).
5. The symbol $\vee$ represents disjunction (or).

STEP 2

For part (a), we need to express the statement "There are students in the library but it is not Friday." in symbolic form. This statement can be broken down into two parts "There are students in the library" and "It is not Friday". The first part corresponds to $q$ and the second part corresponds to $\sim p$ .

STEP 3

The word "but" in the statement can be treated as a logical "and". Therefore, the symbolic form of the statement is $\sim p \wedge q$ .

STEP 4

For part (b), the symbolic form is already given as $\sim p \wedge \sim q$ . This corresponds to the statement "It is not Friday and there are not students in the library."

STEP 5

For part (c), we need to find the descriptive form of the symbolic statement $\sim(p \vee q)$ . This statement can be read as "It is not true that 'it is Friday or there are students in the library'."

STEP 6

The descriptive form of $\sim(p \vee q)$ is "It is not Friday and there are no students in the library."

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QuestionGiven statements $p$ : It is Friday, $q$ : There are students in the library. Fill in symbolic forms for (a) and (b), and descriptive for (c).

Studdy Solution

STEP 1

Assumptions1. $p$ represents the statement "It is Friday." . $q$ represents the statement "There are students in the library."
3. The symbol $\sim$ represents negation (not).
4. The symbol $\wedge$ represents conjunction (and).
5. The symbol $\vee$ represents disjunction (or).

STEP 2

STEP 3

The word "but" in the statement can be treated as a logical "and". Therefore, the symbolic form of the statement is $\sim p \wedge q$ .

STEP 4

For part (b), the symbolic form is already given as $\sim p \wedge \sim q$ . This corresponds to the statement "It is not Friday and there are not students in the library."

STEP 5

For part (c), we need to find the descriptive form of the symbolic statement $\sim(p \vee q)$ . This statement can be read as "It is not true that 'it is Friday or there are students in the library'."

STEP 6

The descriptive form of $\sim(p \vee q)$ is "It is not Friday and there are no students in the library."

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QuestionGiven statements ppp: It is Friday, qqq: There are students in the library. Fill in symbolic forms for (a) and (b), and descriptive for (c).

Studdy Solution

STEP 1

Assumptions1. ppp represents the statement "It is Friday." . qqq represents the statement "There are students in the library."3. The symbol ∼\sim∼ represents negation (not).4. The symbol ∧\wedge∧ represents conjunction (and).5. The symbol ∨\vee∨ represents disjunction (or).

STEP 2

STEP 3

The word "but" in the statement can be treated as a logical "and". Therefore, the symbolic form of the statement is ∼p∧q\sim p \wedge q∼p∧q.

STEP 4

For part (b), the symbolic form is already given as ∼p∧∼q\sim p \wedge \sim q∼p∧∼q. This corresponds to the statement "It is not Friday and there are not students in the library."

STEP 5

For part (c), we need to find the descriptive form of the symbolic statement ∼(p∨q)\sim(p \vee q)∼(p∨q). This statement can be read as "It is not true that 'it is Friday or there are students in the library'."

STEP 6

The descriptive form of ∼(p∨q)\sim(p \vee q)∼(p∨q) is "It is not Friday and there are no students in the library."

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QuestionGiven statements $p$ : It is Friday, $q$ : There are students in the library. Fill in symbolic forms for (a) and (b), and descriptive for (c).

Assumptions1. $p$ represents the statement "It is Friday." . $q$ represents the statement "There are students in the library."
3. The symbol $\sim$ represents negation (not).
4. The symbol $\wedge$ represents conjunction (and).
5. The symbol $\vee$ represents disjunction (or).

The word "but" in the statement can be treated as a logical "and". Therefore, the symbolic form of the statement is $\sim p \wedge q$ .

For part (b), the symbolic form is already given as $\sim p \wedge \sim q$ . This corresponds to the statement "It is not Friday and there are not students in the library."

For part (c), we need to find the descriptive form of the symbolic statement $\sim(p \vee q)$ . This statement can be read as "It is not true that 'it is Friday or there are students in the library'."

The descriptive form of $\sim(p \vee q)$ is "It is not Friday and there are no students in the library."