General Directions. There are four (4) sections to this exam. Please read and fo

Question

General Directions. There are four (4) sections to this exam. Please read and follow all directions carefully. Please do not send your answers in an attachment. Note that ‘->’ is used for conditionals, ‘~’ is used for negations, ‘v’ is used for disjunctions, ‘&’ is used for conjunctions, ‘<->’ is used for biconditionals, and ‘/’ is used as the conclusion indicator.

D. Directions. There are 5 statements below, in English. Translate these statements into symbolic notation using the following translation dictionary: A = the austerity measures work; F = Greece is facing financial ruin; H = Germany will loan Greece more money; J = Spain will loan Greece more money; K = England will loan Greece more money.

1. Greece facing financial ruin is a sufficient condition for the austerity measures not working.

2. Either the austerity measures will work or neither Germany nor Spain will loan Greece more money.

3. Germany won’t lend Greece more money unless the austerity measures work.

4. Spain not lending Greece more money is not a necessary condition for Greece facing financial ruin.

5. Germany and Spain will lend Greece more money only if England doesn’t.

Explanation / Answer

1.

F -> ~A

Finacial ruin implies auteristy measures are not working

2.

A v (~H & ~J)

Either Austerity measures work Or (Germany and Spain won't loan money)

3.

H <-> A

if only if austerity measures works, Germany would lend Greece money

4.

J / F v J / ~F

J conclude the financial ruin or J concludes no finacial ruin

5.

H & J <-> ~K

Germany and Spain will lend if and only if England doesn't

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