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Logic
Truth tables
truth tables for 3 propositions
Equivalence
Implications
100
Statements that may be true or false.
What are propositions?
100
p- t,t,f,f q- t,f,t,f p=>q- t,f,t,t
What is the truth table for p=>q
100
they use p,q, and r
What are truth tables for 3 propositions
100
A equivalence is when two statement use "If and only if."
What does Equivalence mean?
100
A Implications is when two statement use "If...then."
What does Implication mean?
200
False
True or false: Questions are propositions
200
p- t,t,f,f q- t,f,t,f ¬p- f,f,t,t ¬pvq- t,f,t,t
What is the truth table for ¬pvq
200
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
What is the truth table for (p v r) ∧ q
200
I will pass this class, if and only if the teacher is nice.
If p is "I will pass this class" and q is "The teacher is nice." Write p<=>q.
200
If I get all A's, then my dad will buy me a car.
A Implications is when two statement use "If...then."
300
Both B and C
Which of the following are Propositions A) Do we have school tomorrow? B) 100 x 5 = 250 x 2 C) Your hair is black D) Do you have a cell phone.
300
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
What is the truth table for (p v q)=>(p ∧ q)
300
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
What is a truth table for (p => q) v (r v p)
300
I will go out with my family, if and only if i do not have money.
If p is "I will go out with my family" and q is "I have money." Write p<=>¬q.
300
If I have money, then I will buy a car.
If p is "I have money: and q is "I will buy a car." Write p implies q
400
C
What letters are used for Propositions. A) p,q, and t B) r,p, and f C) p,q, and r D) r,p and a
400
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
What is the truth table for ¬p<=>¬q
400
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
What is a truth table for p=>[(¬q v r) <=> (q ∧ p)]
400
I will not play soccer, if and only if it not shining outside.
If p is "I will play soccer" and q is "Its shining outside." Write ¬p<=>¬q
400
¬p=>¬q
Write the Inverse for p=>q
500
A) Some people are not american B) All Cats are not cute C) Dogs are cute
What is the negation of the following: A) Some people are american B) All Cats are cute C) Dogs are not cute
500
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
What is the truth table for (¬p<=>¬q)=> (pvq)
500
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
What is a truth table for [¬(p ∧ q) v (p ∧ r)] ∧ [(¬p v ¬q) => ¬r]
500
¬p<=>q
I will not go to school, if and only if I sleep late. Write the symbols only.
500
If I love you, then we can go out
If ¬p=>¬q is the inverse and p is "I love you " and q is "we can go out." Write the Conditional statement.