1.2 Truth Tables

Question 1

What is a truth table and why is it important?

Answer 1

A truth table is a table that contains all the truth possibilities for a logic statement.

A truth table is important because it can easily show if an argument is valid - i.e. if all the premises are true, then the conclusion has to be true.

Question 2

What is the inclusive or and what is the exclusive or?

Answer 2

The inclusive or includes both statements being true.

The exclusive or is only true when only a single argument is true, not both.

Question 3

How can we make truth tables more compact and what is the main connective of the formula?

Answer 3

You can make a formula more compact by listing the truth values below the corresponding connective symbol in the original formula.

The main connective is the last logic symbol that needs to be evaluated in a formula to get the final truth value.

Question 4

What is an equivalent formula and why is it useful?

Answer 4

Two or more formulas are equivalent if they always have the same truth value, not matter what statements the letters in them stand for and no matter the truth values of those statements.

They are useful because they can simplify complex statements to increase intuition/understanding of a complex statement.

Question 5

What are DeMorgan’s Laws?

Answer 5

~(P ^ Q) = ~P v ~Q

~(P v Q) = ~P ^ ~Q

Question 6

What are Commutative laws?

Answer 6

P ^ Q = Q ^ P

P v Q = Q v P

Question 7

What are Associative Laws?

Answer 7

P ^ ( Q ^ R) = (P ^ Q) ^ R
P v ( Q v R) = (P v Q) v R

Question 8

What are Idempotent Laws?

Answer 8

P ^ P = P

P v P = P

Question 9

What are Distributive Laws?

Answer 9

P ^ (Q v R) = (P ^ Q) v (P ^ R)
P v (Q ^ R) = (P v Q) ^ (P v R)

Question 10

What are Absorption Laws?

Answer 10

P v (P ^ Q) = P
P ^ (P v Q) = P

Question 11

What is the Double Negation Law?

Answer 11

~~P = P

Question 12

What is a tautology?

P ^ a tautology is equivalent to ?

P v a tautology is equivalent to ?

~(a tautology) is a ?

Answer 12

A tautology is a formula that is always true

P ^ a tautology is equivalent to P.

P v a tautology is a tautology.

~(a tautology) is a contradiction.

Question 13

What is a contradiction?

P ^ a contradiction is equivalent to ?

P v a contradiction is equivalent to ?

~(a contradiction ) is a ?

Answer 13

A contradiction is a formula that is always false.

P ^ a contradiction is a contradiction.

P v a contradiction is equivalent to P.

~(a contradiction ) is a tautology.