Symbols
~
What is the symbol for negation? ~
Translate the argument into ordinary English, when
M = I am a member of a club.
W = the club is willing to have me
J = I join the club
M > (W * J) W> ~J :: ~M
What is... I am a member of a club only if the club is willing to have me, and I join it. I do not join any club if the club is willing to have me. So, I am not a member of a club.
Double Negation (D.N.)
What is...
p = ~~p
Symbolize Modus Ponens (M.P.)
What is...
p > q
p
:: q
A step by step deduction of a conclusion from a set of premises, each step being justified by an appropriate basic rule
What is a formal proof of validity?
Fill in the blank: A __________ is true when both are true.
Conjunction (*)
Translate the following argument into symbolic form using the symbols C, N, P:
The bank bill was constitutional if and only if it was both necessary and proper. The bank bill was proper. There, the bank bill was constitutional.
C = (N*P) P :: C
Symbolize the rule of replacement: Tautology.
p = (p v p)
p = (p * p)
p
q
:: p * q
is the rule of ____________.
What is conjunction?
a valid argument form which can be used to justify steps in a proof.
What is a rule of inference?
The symbol for disjunction.
What is v ?
Translate the argument into symbolic form for a proof, using B, P :
Bill is guilty of burglary if and only if he did not have permission to take the goods. Bill had permission to take the goods. Therefore, Bill is not guilty of burglary.
B = ~P
P / ::~B
What is the rule of transposition?
(p > q) = (~q > ~p)
(p > q) * (r > s)
p v r
:: q v s
Constructive Dilemma
True or False: Each step in a proof is usually used at some step later in the proof
True
This symbol can be translated as "if and only if" as well as "is equivalent to..."
What is a biconditional or = ?
Justify the steps in the proof using the rules of inference or replacement:
1. A v B
2. A > C
3. ~C / ::B
4. ~A __________
5. B __________
4. 2, 3 M.T.
5. 1, 4 D.S.
Fill in the blank: ______________ is symbolized:
(p v q) = (q v p)
(p* q) = (q * p)
What is Commutation?
p * q
:: p
symbolizes which rule of inference?
What is simplification (simp)?
A set of forms of equivalent statements
Rules of replacement
This logical operator is composed of two parts and translated as, "if... then..." Name the operation and its parts.
What is a conditional (>), with an antecedent and a consequent.
Justify the steps in the proof using the rules of inference of replacement:
1. (D > E) * (F > E)
2. F v D / :: E
3. D v F __________
4. E v E __________
5. E __________
3. 2 Com.
4. 1, 3 C.D.
5. 4 Taut.
Fill in the blank: ____________ is symbolized:
~ (p * q) = (~p v ~q)
~(p v q) = (~p * ~q)
What is De Morgan's Theorems (De. M.)
Name the rule of inference and its parts:
p > q
q > r
:: p > r
Hypothetical Syllogism (H.S.); antecedent, consequent
Fill in the blank: _____________ propositions have identical truth values and can replace eachother whenever they occur.
What is Equivalent?