Test 1

Question 1

¬

Answer 1

NOT, Negation, inverses value, T becomes F, F becomes T.

Question 2

∧

Answer 2

AND, Conjunction, both have to be true.

Question 3

∨

Answer 3

Inclusive OR, disjunction, if either is true the compound statement is true.

Question 4

⊕

Answer 4

Exclusive OR (XOR), exclusive disjunction, only true if ONE statement true but not both.

Question 5

↔

Answer 5

If and only if (IFF), biconditional, only true if both values the same, 2T or 2F.

Question 6

→

Answer 6

Implies, conditional, only false if true implies false.

Question 7

How to prove something is a WFF?

Answer 7

1. Show individual atoms are WFF e.g p, q, r
2. If the atoms are WFF so too are (¬p) (p∧q) etc.
3. Keep expanding for the whole example.

Question 8

What is De Morgan’s Law?

Answer 8

A way of pushing ¬ inside brackets.
e.g ¬(p∧q) becomes ¬p ∨ ¬q.
The ¬ goes in front of the atoms, AND switch to OR,
OR switches to AND.

Question 9

What is double negation?

Answer 9

When there are 2 NOTs together so they cancel out.

eg ¬¬P ≡ P

Question 10

≡

Answer 10

Logically equivalent, relationship between WFFs, not a logical connective

Question 11

Tautology

Answer 11

All outputs true

Question 12

Satisfiable

Answer 12

At least 1 output true.

Question 13

Contradiction

Answer 13

All outputs false.

Question 14

What logical connectives can generate all truth tables?

Answer 14

¬, ∧, V

Question 15

Associativity

Answer 15

When you have the same connective (all ∧ or V) then you don’t need brackets because of associativity.

Question 16

Commutativity

Answer 16

p∧q ≡ q∧p and pVq ≡ qVp

Question 17

Idempotence

Answer 17

p∧p ≡ p and pVp ≡ p

Question 18

Distributivity

Answer 18

p∧(q∨r) ≡ (p∧q)∨(p∧r) and p∨(q∧r) ≡ (p∨q)∧(p∨r)

Question 19

Absorption

Answer 19

p ∨ (p ∧ q) ≡ p and p ∧ (p ∨ q) ≡ p

Question 20

|=

Answer 20

Semantic turnstile. If on the left of a WFF it means it is a tautology, if on the right of a WFF means it is a Contradiction

Question 21

How to show 2 WFF are logical equivalents?

Answer 21

WFF A ≡ WFF B if and only if |= A ↔ B (a tautology)

Question 22

Contingency

Answer 22

A WFF that is sometimes true and sometimes false

Question 23

What does Satisfy the WFF mean?

Answer 23

A truth assignment that makes a WFF true is said to satisfy the WFF.

Question 24

What does falsify the WFF mean?

Answer 24

A truth assignment that makes a WFF false is said to falsify the WFF.

Question 25

The Satisfiability Problem

Answer 25

(SAT) Given a wff in PL, decide whether there is some truth assignment to the atoms that make the wff take the value true. A program that solves SAT is called a SAT solver.

Question 26

Statement

Answer 26

A Sentence that can be true or false.

Question 27

Compound statement

Answer 27

Statements glued together with logical connectives so the T or F can be calculated.

Question 28

How to figure out how many rows a truth table will have?

Answer 28

2^n where n is the number of atoms.

Question 29

∴

Answer 29

Therefore