Propositional Logic

Question 1

How to construct truth table?

Answer 1

1. Create table with 2^n rows with n columns
2. Fill in the first n columns with all the possible combinations

Question 2

What is Disjunction?
p ∨ q

Answer 2

p ∨ q is True
when
BOTH p AND q are False

Question 3

What is Conjunction?
p ∧ q

Answer 3

p ∧ q is True
when
BOTH p AND q are True

Question 4

What is Negation?
¬p

Answer 4

¬p is not p

Question 5

p → q

Answer 5

If p, then q

E.g.
p (T) , q (T) then p → q (T)
p (T) , q (F) then p → q (F)
p (F) , q (ANY) then p → q (T)

Question 6

What is XOR (Exclusive-OR)
p ⊕ q

Answer 6

p ⊕ q is True
when
EITHER p OR q is true

Question 7

p ↔ q

Answer 7

p if and only q
p → q AND q → p

Question 8

p ≡ q

Answer 8

p and q have same truth value

Question 9

Let p,q be propositions
A be conditional statement,
p → q

What is the converse of A?

Answer 9

q → p

Question 10

Let p,q be propositions
A be conditional statement,
p → q

What is the contrapositive of A?

Answer 10

¬q → p

Contrapositive:
Negate second, then Negate first
(basically negate both then change position)

Question 11

Let p,q be propositions
A be conditional statement,
p → q

What is the inverse of A?

Answer 11

¬p → ¬q

Inverse:
Just negate both. Don’t switch position.