Elementary Logic; Boedeker; Fall 2004. Conditional statements
Standard form of conditional statement:
If R, then S.
R is the antecedent of the conditional, and a sufficient condition of S.
S is the consequent of the conditional, and a necessary condition of R.
R: It rains
S: The streets get wet
A “truth-table” for a conditional statement:
R S
t t t
t f f
f t t
f t f
Non-standard form of conditional statement:
A only if B.
This statement in standard form:
If A, then B.
A is the antecedent of the conditional, and a sufficient condition of B.
B is the consequent of the conditional, and a necessary condition of A.
(remember: “only if…” = “… is a necessary condition” = “…” is the consequent)
Another non-standard form of conditional statement:
Only if C occurs will D occur.
This statement in standard form:
If D will occur, then C occurs.
Exercises:
Translate the following sentences into the standard (= “if…, then___”) form for conditional
statements. If the sentence implicitly involves the quantifier “all”, then use the variable “s” for
the person(s) in question (in such a case, “s” should occur in both the antecedent and the
consequent):
- Winning the majority of Electoral College votes is sufficient for being elected President.
- Questioning Dubyuh’s foreign policy is sufficient for being a terrorist.
- Maintaining a strong military is necessary for domestic security.
Translate the following statements in two ways: first into standard form, and then using either “is
a necessary condition for” or “is a sufficient condition for”:
- There will be world peace only if the United Nations remains strong.
- The world will go to hell in a handbasket if Dubyuh isn’t elected.
- For Ralph Nader to be elected President, he will need to gain a majority of the votes in the
Electoral College.
- It would take a miracle for Ralph Nader to be elected President.
- The U.S. can win the “war on terrorism” only by invading Iran and North Korea.
- Al Qaeda will remain strong if Osama Bin Laden remains at large.
- In order for someone to be President, s/he must have been born in the United States.
- You need either to be rich or to have rich friends to become President.
- Someone can be President only if s/he is at least 35 years old.
- Only an economic girlie man would be pessimistic about the U.S. economy.