Equivalent Compound Statements

Conjuntion

100

form:                 p and q   =  q and ___

P

200

negation:           p and q =    not p and ___  __

not q

300

Antecedent (P) to "All have sinned and fall short of the glory of God, "

P= All have sinned

400

The logical operator used for conjunctions

AND

500

Kelleigh and Belle went to the picnic. 

Give an equivalent statement in the conjunction form.

Belle and Kelleigh went to the picnic.

Disjunction

100

1. form:         p or q    = q or _____

P

200

dusjunction uses this logical operator

OR

300

negation :  Not p or q = ____p and ___q

Not; not

400

the consequent in "To his own master he stands or falls." (hint: p or q)

falls

500

What kind of disjunction statement do we call this?  Look at the highlighted sections to help?

There was no way to turn either to the right or to the left.  =

There was no way to turn right and then there was no way to turn left. 

    He could neither turn right or left.

negation or Neither-nor statment

Conditional and Bi-Cond

100

conditional form:        if p then q     =  if ___ q then not P

not

200

another conditional form: 

If p then q = p and ____q 

not

300

 the logical operator for bi-conditional

If and only if

400

form:        p ____ and _____ if q  = if p then q and if q then p

if; only

500

complete the bi-conditional statement: 

A number is even if and only if its square is even.

If a number is even then its square is even and if its square is even then a number is even.

A number and its square are both even or __________

they are both not even

Try it out

100

use square of opposition:

1. all planets are ringed planets 

2. no planets are ringed planets

these statements show what relationship

contrariety (aka: inconsistency)

200

use square of opposition:

1. some planets are ringed planets 

2. no planets are ringed planets

these statements show what relationship

contradiction

300

Negate this Conditional: "If we die with Christ, we shall be raised with Him"  

We die with Christ and/but we shall not be raised with him

400

equivalent conditional statement : "If we die with Christ, we shall be raised with Him" .  

Use the "if not q then not p form" (it's like contrapositive form) 

If we shall not be raised with christ, then we do not die with Him"

500

Using square of opposition: The subaltern to "no planets are ringed planets

some planets are not ringed planets

General lines of proof

100

One of Aristotle's general lines of proof

opposites

correlative ideas

rational correspondence

a fortiori

200

pairs: give/take, buy/sell

correlative ideas

300

how much more argument

a fortiori

400

We establish truth in three steps

1. define (terms)

2. make accurate statements

3. make logical arguments 

500

 "the way of a fool is right in his own eyes, but he who heeds counsel is wise"

 opposites