Propositional Logic

What is a proposition that is always false?

• Negation

• Tautology

• Contradiction

• Absolute

p and q are both true propositions and r is a false proposition.

What is the truth value of ~r

• true

• false

• neither true nor false

• information is insufficient

p and q are both true propositions and r is a false proposition.

What is the truth value of  $q\wedge\left(\sim r\right)$  ?

• true

• false

• neither true nor false

• information is insufficient

p and q are both true propositions and r is a false proposition.

What is the truth value of  $p\vee\left(q\wedge\left(\sim r\right)\right)$  ?

• true

• false

• neither true nor false

• information is insufficient

p and q are false and r is true.

What is the truth value of  $\sim p$  ?

• true 

• false

• neither true nor false

• information is insufficient

p and q are false and r is true.

What is the truth value of  $q\leftrightarrow r$  ?

• true 

• false

• neither true nor false

• information is insufficient

p and q are false and r is true.

What is the truth value of  $\left(\sim p\right)\wedge\left(q\leftrightarrow r\right)$  ?

• true 

• false

• neither true nor false

• information is insufficient

Determine the truth values of the propositions p, q, and r that will make  $p\wedge\left(q\vee r\right)$  false:

• p, q, and r are all true or all false

• p and r are false, while q is true.

• If p is true, q and r are both false. If P is false, each of q and r may either be true or false.

• If p is true, q and r are both true. If p is false, each of q and r may either be true or false

Determine the truth values of the propositions p, q, and r that will make  $\left(p\wedge q\right)\vee r$  false:

• q should be false. p and r may either be both true or both false.

• p should be false. Either q is true and r is false, or vice versa, or both are true.

• p and q should be false. r may be true or false.

• r should be false. p and q may take any truth value except for both are true.

Determine the truth values of the propositions p, q, and r that will make  $\sim\left(p\wedge\left(\sim q\right)\right)$  false:

• p and r should be false, while q should be true.

• p and q should be false, while r should be true.

• q should be false, while p and r should be true.

• q and r should be false, while p should be true.