Logic

The disjunctiondisjunction p logical or∨ q is false false only when both p and q are​ _______.

FALSE

Use the truth table to determine the set of conditions that make the compound statement true. Choose the correct answer below.

The statement is true whenever p is true or q is falsep is true or q is false​, and is false otherwise.

The conjunction is symbolized by logical and∧ and is read​ "_______."

and

The biconditional is symbolized by left right arrow↔ and is read "

if and only if

The conditional is symbolized by right arrow→ and is read

if, then

Let p and q represent the following simple statements. ​p: The chair is brokenThe chair is broken. ​q: It is snowing outsideIt is snowing outside. Write the symbolic statement tilde left parenthesis q logical or p right parenthesis~(q∨p) in words.

it is not true that it is snowing outside or the chair is broken

The negation is symbolized by​ ~ and is read​ "_______."

not

The disjunction is symbolized by logical or∨ and is read​ "_______."

or

Let​ p, q, and r represent the following statements. ​p: It is time to sleepIt is time to sleep. ​q: It is lateIt is late. ​r: Upper I am tiredI am tired. Write the following compound statement in its symbolic form. If Upper I am tiredI am tired and it is lateit is late​, then it is time to sleepit is time to sleep.

p(r∧q)→p.

Let​ p, q, and r represent the following simple statements. ​p: Upper I eat bananasI eat bananas. ​q: The taxes are highThe taxes are high. ​r: Upper I studyI study. Write the following compound statement in its symbolic form. Upper I eat bananasI eat bananas and the taxes are highthe taxes are high​, or Upper I studyI study.

r(p∧q)∨r.

Let p and q represent the following statements. ​p: The stove is hotThe stove is hot. ​q: The soup is coldThe soup is cold. Write the following compound statement in its symbolic form. The soup is not coldThe soup is not cold if and only if the stove is hotthe stove is hot.

~q (arow both sides) p

Write the statement in symbolic form. Let p and q represent the following statements. ​p: The teacher is at the blackboard.The teacher is at the blackboard. ​q: The students are at their desks.The students are at their desks. The students are not at their desks or the teacher is not at the blackboard.The students are not at their desks or the teacher is not at the blackboard.

~qV~p

Write the following compound statement in its symbolic form. and it is snowing outside it is snowing outside.

​p^q