Practice ~B ((B D) D) tf-true? (M ~N) & (M N)tf-false? (B H) & (B ~H)tf-false, true or indeterminate? (C & (B A)) and ((C&B)

Practice

~B ((BD) D) tf-true?(M ~N) & (M N) tf-false?(BH) & (B~H) tf-false, true or indeterminate?(C & (BA)) and ((C&B) A) tf-equivalent?{B&F, ~(B&G)} G ?

Symbolization techniques

Identify component propositions



The rent is due, and I have no money.



The rent is due, and I have no money.

The rent is due.I have no money.



If the cat’s away, the mice will play.




The cat is away (C)The mice will play (M)




The cat is away (C)The mice will play (M)

C M



Either the guest of honour wore brown, or he fell in the mud on the way to the party.




The guest of honour wore brown (B)The guest of honour fell in the mud on the way to the party (M)




The guest of honour wore brown (B)The guest of honour fell in the mud on the way to the party (M)

B M



Sue and Tim are happy



Sue and Tim are happy

Sue is happy (S)Tim is happy (T)

S & T



Sue and Tim are happy, and they are throwing a party.









Sue is throwing a party. (S1) (?)Tim is throwing a party. (T1) (?)

They are throwing a party. (P) (?)





Sue is throwing a party. (S1) (?)Tim is throwing a party. (T1) (?)

They are throwing a party. (P) (?)

(S&T) & (S1 & T1)(S&T) & P



Sue and Tim are getting married.



Sue and Tim are getting married.

MS & T


Conjunction

An explicit form of a conjunction: Sue is happy and Tim is happy – S & T


Conjunction


These are also conjunctions:A but BA however BA although BA nevertheless BA nonetheless BA moreover B


Conjunction


These are also conjunctions:A but BA however BA although BA nevertheless BA nonetheless BA moreover B

She is poor, but honest. (P&H)A disjunction has two components, while

a negation has only one. (D&N)


She is poor (P)It is true that she is poor (P)

She certainly is poor (P)She certainly is poor (P)She certainly is poor (P)


Negation

Explicit form:It is not the case that ...


Negation


It is not the case that the temperature is rising


Negation


It is not the case that the temperature is rising

The temperature is rising (R)


Negation


It is not the case that the temperature is rising (~R)



Negation


It is not the case that the temperature is rising (~R)


It is false that the temperature is risingThe temperature is not rising


Disjunction

Explicit form:Either … or …


Disjunction


She’s either a lunatic or a genius.


Disjunction


She’s either a lunatic or a genius.

Either she is a lunatic, or she is a geniusL G


Material Conditional

Explicit form:If …, then…




These are also conditionals equivalent to ‘If A, then C’ (AC):

If A, CC, if AC, provided that AC, given AA only if C






If these shoes go on sale, I’ll buy two pairsS B






Only ifs

I will go camping this weekend if I finish my workI will go camping this weekend only if I finish my work






Only ifs

I will go camping this weekend if I finish my workI will go camping this weekend only if I finish my work

If you buy a ticket, you will win the lotteryOnly if you buy a ticket, you will win the lottery






Only ifs

I will go camping this weekend if I finish my workF C

I will go camping this weekend only if I finish my workC F

If you buy a ticket, you will win the lotteryT W

Only if you buy a ticket, you will win the lotteryW T


Material Biconditional

Explicit form:… if and only if …




If a conjunction is true, then both conjuncts are true (C B)A conjunction is true only if both conjuncts are true (B C)




If a conjunction is true, then both conjuncts are true (C B)A conjunction is true only if both conjuncts are true (B C)If a conjunction is true, then both conjuncts are true, and it

is true only if both conjuncts are true ( (C B) & (B C) )




If a conjunction is true, then both conjuncts are true (C B)A conjunction is true only if both conjuncts are true (B C)If a conjunction is true, then both conjuncts are true, and it

is true only if both conjuncts are true ( (C B) & (B C) )Both conjuncts are true if and only if the conjunction is true

( B C )




Sue is married to Tim if and only if Tim is married to Sue ( S T )




These are also biconditionals equivalent to A B:

A if but only if BA just in case B


Neither… nor…

explicit form: both it is not the case that A and it is not the case that B:

~A & ~B


Neither… nor…


~A & ~B

Neither Sue not Tim are throwing a party~S & ~T


Neither… nor…


~A & ~B


Also correct symbolization is ~ (S T)


Neither… nor…


~A & ~B


Also correct symbolization is ~ (S T)

De Morgan’s Laws:~ (A&B) (~A ~B)~ (AB) (~A & ~B)


Not both ... and ...

explicit form: it is not the case that both A and B:

~ (A & B)




~ (A & B)

Not both Sue and Tim are throwing a party~ (S & T)




~ (A & B)

Not both Sue and Tim are throwing a party~ (S & T)

Also correct symbolization is ~S ~T,because of De Morgan’s Laws:

~ (A&B) (~A ~B)~ (AB) (~A & ~B)


… unless …

explicit form: either A or B

if it is not the case that A then Bif it is not the case that B then A


… unless …

explicit form: either A or B

if it is not the case that A then Bif it is not the case that B then A

You and I can be friends unless you take advantage of meF A

~ A F~ F A

Practice ~B ((B D) D) tf-true? (M ~N) & (M N)tf-false? (B H) & (B ~H)tf-false, true or indeterminate? (C & (B A)) and ((C&B)

Documents

happy tsue

happy s tthese

brown bthe guest of

poor pshe

poor pit

cthe mice

b bd d tftrue

cb atfequivalent