Logic

Question 1

Define Logically vaid

Answer 1

An argument is logically valid iff there is no possible situation in which its premises are all true and its conclusion false

Question 2

Define counterexample

Answer 2

A counterexample to an argument is a possible situation in which all the premises of the argument are all true and its conclusion false

Question 3

Define truth functional

Answer 3

A connective is truth functional if the truth value of the complex sentence built up using the connective is completely determined by the truth values of the simpler sentences from which it is built

Question 4

Define logical truth

Answer 4

A sentence is a logical truth iff it is true in every possible situation

Question 5

Define contradiction

Answer 5

A sentence is a contradiction iff it is false in every possible situation

Question 6

Define logical possibility

Answer 6

A sentence is a logical possibility iff there is at least one possible situation in which it is true

Question 7

Define logical equivalent

Answer 7

Two sentences are logically equivalent iff they have the same truth value in every possible situation

Question 8

Define a truth functionally complete

Answer 8

A set of truth functional connectives is truth functionally complete iff the connectives in question allow us to express all truth functions

Question 9

When is a system of proof sound

Answer 9

A system of proof is said to be sound iff if x₁,……, x_n | y then y is a logical consequence of x₁,……, x_n​

Question 10

When is a system of proof complete

Answer 10

A system of proof is said to be complete iff if y is a logical consequence of x₁,……, x_n​ then x₁,……, x_n | y​

Question 11

State the and proof rules

Answer 11

Question 12

State the or proof rules

Answer 12

Question 13

State the contradiction proof rules

Answer 13

Question 14

State the negation proof rules

Answer 14

Question 15

State the implies proof rules

Answer 15

Question 16

State the iff proof rules

Answer 16

Question 17

What is an equivalent statement to for all x(f(x) –> g(x))

Answer 17

there doesnt exist x(f(x) and not g(x))

Question 18

What is an equivalent statement to there exist x(f(x) and g(x))

Answer 18

there exist x (g(x) or not f(x))

Question 19

state the for all proof rules

Answer 19

Question 20

state the existence proof rules

Answer 20

Question 21

How do we show a new connective is truth functional

Answer 21

if we can make the and, or and not tables