logic week 1 - 4 (test 1)

Question 1

necessary truth

Answer 1

• no possibility where it is false

Question 2

possible truth

Answer 2

• there is a possible world where it is true

Question 3

good argument

Answer 3

• arguments that are sound and valid

Question 4

validity

Answer 4

• if and only if its impossible for the premises to be true and the conclusion false
• the truth of the premises guarantees the truth of the conclusion

Question 5

sound

Answer 5

• valid and true premises

Question 6

circularity

Answer 6

• one of the premises is the same as the conclusion
• always sound and valid args

Question 7

consistency

Answer 7

• it is possible for all sentences to be true
• has close relationship with validity

Question 7

formal validity

Answer 7

• if and only if every argument with this form is valid
• can have generally valid args that are valid based purely off of the link between concepts of arg but formal validity is constant by form (recipe)

Question 8

conditional

Answer 8

• if … then … (and other English forms)
• hook
  -truth function rule ; false if we move from truth to falsity

Question 9

conjunction

Answer 9

• … and …
• dot
• truth function rule ; true only if both are true

Question 10

disjunction

Answer 10

• … or …
• inclusive or for this course
• vel
• truth function rule ; false only if both are false

Question 11

negation

Answer 11

• not …
• tilde
• truth function rule ; one is true opposite isn’t

Question 12

biconditional

Answer 12

• = (p hook q) . (q hook p)
• shortened to if and only if = iff
• truth function rule ; true in doubles (two false or two truths)

Question 12

tautology

Answer 12

• statement true no matter the components truth-values

Question 13

contigent statement

Answer 13

• sometime true sometimes false

Question 14

contradiction

Answer 14

always false

Question 15

proving validity

Answer 15

• assume concl. is false and premises true then do working. if possible then invalid if not possible then valid

Question 16

proving consistency

Answer 16

• set all sentences to be true if letters allow for such then consistent if not inconsistent

Question 17

logical equivalence and logical implication

Answer 17

• method 1: focus on true state and balance it on rhs + lhs
• method 2: focus on falsity state and balance it on rhs + lhs
• method 3: side based focus & truth/falsity consistency

Question 18

equivalence argument forms

Answer 18

• DN ; not not a = a
  -** DeM** ; distribute negation in and change to and/or = take out negation and change to and/or
• comm; swap around and/or brackets order
• assoc; and/or can move small bracket if within bigger bracket with strictly and in it or strictly or in it
• dist; distribute the and/or and make two brackets with opp of distributed operator = ‘factorise out’ and or and replace with bracket of opposite and/or
• contra; normal hook = negated and swaped order hook
• impl; normal hook = negation of first bit and vel replacement of hook
• exp; peep answer sheet bc i cant put it in words
• taut; statement = statement and/or same statement
• equiv; biconditional = normal expansion or biconditional = [(p.q) v same bracket but distributed negation]

these are given to you but wise to learn them off dome

Question 19

sentential proofs

Answer 19

• MP
• MT
• DS
• HS
• SIMP
• CONJ
• ADD
• CD