Show:
Vocabulary & Equivalence
Implications
Symbols
Truth tables
Truth tables for 3 propositions
100
What does Equivalence mean?
A equivalence is when two statement use "If and only if."
100
What does Implication mean?
A Implications is when two statement use "If...then."
100

What is a biconditional statement?

If and only if statements

100
Create a Truth table for p=>q
p- t,t,f,f q- t,f,t,f p=>q- t,f,t,t
100
What are truth tables for 3 propositions
they use p,q, and r
200
If p is "I will pass this class" and q is "The teacher is nice." Write p<=>q.
I will pass this class, if and only if the teacher is nice.
200
If p is "I get all A's" and q is "My dad will buy me a car." Write p=>q
If I get all A's, then my dad will buy me a car.
200

What is the notation for a conjunction?

P (upside down V) Q

200
Create a Truth table for ¬pvq
p- t,t,f,f q- t,f,t,f ¬p- f,f,t,t ¬pvq- t,f,t,t
200
Create a truth table for (p v r) ∧ q
p- t,t,t,t,f,f,f,f q- t,t,f,f,t,t,f,f r- t,f,t,f,t,f,t,f (p v r)- t,t,t,f,t,t,t,f (p v r) ∧ q- t,t,f,f,t,t,f,t
300

A compound statement that is always false

Self-Contradiction

300
If p is "I have money: and q is "I will buy a car." Write p implies q
If I have money, then I will buy a car.
300

What is the name of this symbol?

V

Disjunction

300
Create a Truth table for (p v q)=>(p ∧ q)
p- t,t,f,f q- t,f,t,f pvq- t,t,t,f p∧q- t,f,f,f (pvq)=>(p∧q)- t,f,f,t
300
Create a truth table for (p => q) v (r v p)
p- t,t,t,t,f,f,f,f q- t,t,f,f,t,t,f,f r- t,f,t,f,t,f,t,f (p => q)- t,t,f,f,t,t,t,t (r v p)- t,t,t,t,t,f,t,f (p => q) v (r v p)- t,t,t,t,t,t,t,t
400

A compound statement that is always true

Tautology
400
Write the Inverse for p=>q
¬p=>¬q
400
What is the name of the gate that is only true when A and B are false?  Provide the name and draw it.

NOR gate

400
Create a Truth table for ¬p<=>¬q
p- t,t,f,f q- t,f,t,f ¬p- f,f,t,t ¬q- f,t,f,t ¬p<=>¬q- t,f,f,t
400
Create a truth table for p=>[(¬q v r) <=> (q ∧ p)]
p- t,t,t,t,f,f,f,f q- t,t,f,f,t,t,f,f r- t,f,t,f,t,f,t,f ¬q- f,f,t,t,f,f,t,t (¬q v r)- t,f,t,t,t,f,t,t (q ∧ p)- t,t,f,f,f,f,f,f [(¬q v r) <=> (q ∧ p)]- t,f,f,f,f,t,f,f p=>[(¬q v r) <=> (q ∧ p)]- t,f,f,f,t,t,t,t
500
I will not go to school, if and only if I sleep late. Write the symbols only.
¬p<=>q
500
If ¬p=>¬q is the inverse and p is "I love you " and q is "we can go out." Write the Conditional statement.
If I love you, then we can go out
500

Draw and name the logic gate that is true only when both are true or both are false.

XNOR gate

500

Create a Truth table for (¬p<=>¬q)=> (pvq)

p- t,t,f,f q- t,f,t,f ¬p- f,f,t,t ¬q- f,t,f,t (¬p<=>¬q)- t,f,f,t (pvq)- t,t,t,f (¬p<=>¬q)=> (pvq)- t,t,t,f

500
Create a truth table for [¬(p ∧ q) v (p ∧ r)] ∧ [(¬p v ¬q) => ¬r]
p- t,t,t,t,f,f,f,f q- t,t,f,f,t,t,f,f r- t,f,t,f,t,f,t,f ¬p- f,f,f,f,t,t,t,t ¬q- f,f,t,t,f,f,t,t ¬r- f,t,f,t,f,t,f,t (p ∧ q)- t,t,f,f,f,f,f,f ¬(p ∧ q)-f,f,t,t,t,t,t,t (p ∧ r)- t,f,t,f,f,f,f,f ¬(p ∧ q) v (p ∧ r)- t,f,t,t,t,t,t,t (¬p v ¬q)- f,f,t,t,t,t,t,t (¬p v ¬q) => ¬r- t,t,t,f,t,f,t,f [¬(p ∧ q) v (p ∧ r)] ∧ [(¬p v ¬q) => ¬r]- t,f,t,f,t,f,t,f