## Proof by Contradiction with Resolution

For the problems given below,
use resolution and proof by contradiction to prove
the conclusion from the premises given.
Show all work, including the logical expression that corresponds
to each premise, the conversion of each logical expression to
conjunctive normal form, and each step in the proof
(and the inference rule used).

### Spring Flowers

If the advertisement is correct, then if the seeds are planted
in April then the flowers bloom in July.
The seeds are planted in April.

Prove that if the flowers do not bloom in July, then the
advertisement is not correct.

### Commodities and Inflation

If a scarcity of commodities develops, then prices rise.
If there is a change in administration, then fiscal controls
will not be continued.
If the threat of inflation persists,
then fiscal controls will be continued.
If there is overproduction, then prices do not rise.
Either there is overproduction or there is a change of administration.

Prove either a scarcity of commodities does not develop,
or the threat of inflation does not persist.

### Gainful Employment vs. the Alternatives

If you work then you earn money,
but if you are idle then you enjoy yourself.
Either you work or you are idle.
However, if you work then you do not enjoy yourself,
while if you are idle then you do not earn money.

Prove that you enjoy yourself if and only if you do not earn money.

**Hint:** The phrase "A if and only if B"
means A implies B and B implies A.

### Due Date

This assignment is due on Tues Apr 13th **at the start of class**.
Any assignment turned in after class begins is at least one day late!