Unit 1 - Propositional Logic

Question 1

Explain what would make a proposition a tautology

Answer 1

A proposition is a tautology if it is true for all combinations of truth values

Question 2

What would be the truth table results for p => q (p implies q)

Answer 2

T, T, F, T

True if both p and q are True, or p is False

p | q | p ⇒ q
F | F | T
F | T | T
T | F | F
T | T | T

Question 3

Define a proposition

Answer 3

A proposition is a statement that can be meaningfully considered True or False

Question 4

What are truth values (for a proposition)

Answer 4

they are the two basic propositions True and False;

Question 5

What are propositional letters

Answer 5

denoted with the symbols p, q,r,s. They work as placeholders for propositions

Question 6

What are the logical operators

Answer 6

denoted with the symbols ∧, ∨, ¬ , ⇒. And, Or, Not and Implication

Question 7

the proposition p ∧ q is True

Answer 7

only when both p and q are True;

Question 8

the proposition p ∨ q is False

Answer 8

only when both p and q are False

Question 9

the proposition p ⇒ q is False only when

Answer 9

p is True and q is False;

Question 10

The intuitive meaning of p ⇐⇒ q is

Answer 10

if p then q, and if q then p.

Question 11

The important property of the proposition p ⇐⇒ q is that

Answer 11

it is true only when p and q are either both
true, or both false

Question 12

we say that q is a tautology if

Answer 12

q is true for all combinations of truth values
assigned to p1, p2, . . . , pn;

Question 13

we say that q is a contradiction

Answer 13

if q is false for all combinations of truth values
assigned to p1, p2, . . . , pn.