Study Guide on Translating Conditionals

Symbolic Logic I

Study Guide on Translating Conditionals

Proper translation of conditionals from ordinary English into proper symbolic notation is both critical and difficult. Below are two lists, one of words and phrases that precede the antecedent of a conditional, the other of words and phrases that precede the consequent. Use these terms to help you identify the parts of a conditional.

Terms that precede the antecedent: Terms that precede the Consequent:

IfThen

Given thatOnly if

Insofar asIt follows that

Provided thatImplies

So long asLeads to

In caseMeans that

Follows fromIs a sufficient condition for

Is implied by

Whenever

Is a necessary condition for

NOTE: Sufficient conditions are antecedents of conditionals. Necessary conditions are consequents of conditionals. If one statement is both necessary and sufficient for another, then the relation between those statements is that of the biconditional.

1. Which of the following expressions should be translated as "p q"?

a. q, if pyesb. q implies p no c. q follows from p yes

d. q, only if p noe. q is necessary for p yesf. p only if q yes

g. p, if only q noh. q is sufficient for p noi. p implies qyes

2. Translate each of the following English sentences into proper symbolic notation.

a. QUAYLE will be elected only if either JACOBS is nominated by the Democrats or KEMP doesn't run.

Q  (J  ~K)

b. A 'no' from ONE of us means a 'no' from BOTH of us. (A parental lecture)

O  B

c. You will PASS the course and GRADUATE unless you either DISRUPT the class or otherwise IRRITATE the professor.

(P  G)  (D  O)

d. That either you will PASS the exam or you will not STUDY hard follows from the fact that you will not both study hard and not pass the exam.

~(S  ~P)  (~S  P)

e. If both JAMES and HELEN are in class today, then if MARK is in class too, either BOB or SUE won't be.

(H  J)  [M  (~B  ~S)]

3. Express each of the following English sentences as a conditional. Do not worry about symbolizing them at this time.

a. Every multiple of FOUR is a multiple of TWO. If a number is a multiple of four, then it is a multiple of two.

b. The game will be CANCELED in the event of RAIN. If it rains, the game will be canceled.

c. Two integers whose SUM is seven cannot both be EVEN.If the sum of two integers is seven, then it is not the case that both of then can be even.

d. UNC's BEATING Louisville proves that UNC is the better TEAM. If UNC beats Louisville, then UNC is the better team