Skula's Logic Extravaganza

Biconditionals/Writing Statements

100

What is a Biconditional Statement?

A two way statement that uses "If and only if."

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.

300

If p is "I will go out with my family" and q is "I have money." Write p<=>~q.

I will go out with my family, if and only if i do not have money.

400

If p is "I will play soccer" and q is "Its shining outside." Write ~p<=>~q

I will not play soccer, if and only if it not shining outside.

500

I will not go to school, if and only if I sleep late. Write the symbols only.

~p<=>q

Conditionals

100

How can we prove that a conditional statement is false?

How do we know when a conditional is false in a truth table?

For Sentence-based problems: When we can locate a counter-example (different q) 

Using Truth Tables: When p is true and q is false (TF)

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.

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.

400

What is the negation of p->q 

"If I go to Miami, then I will be at the beach"

Negation p^~q

I am at Miami and I am not at the beach

500

Write the negation of 

"All students are A students"

SOME students are NOT A students

Statements and negations

100

What is a Statement?

A declarative statement that is either true or false, but not both true and false

200

What words match the following symbols?

~ = 

^ =

V = 

-> =

<-> = 

Not

And

OR

If, then

If and only if

300

Which of the following are Statements A) Do we have school tomorrow B) 100 x 5 = 250 x 2 C) Your hair is black

B and C

400

What letters are use for statements? A) p,q, and t B) r,p, and f C) p,q, and r D) r,p and a

C

500

Write the negation of the following: A) Some people are american B) All Cats are cute C) Dogs are no cute

A) Some people are not american B) All Cats are not cute C) Dogs are cute

Truth tables 2 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

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

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

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

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,f,f,t (¬p<=>¬q)=> (pvq)- t,t,t,t

Truth tables for 3 statements

100

Truth Tables that involve three statements use the letters ____, ____, and ____ AND the table has ___ rows instead of 4.

p, q, r, 8

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

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

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

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