Question

Translate the following ordinary-language sentences into logical symbolic form using capital letters for simple phrases and the standard symbols – “·,” “˅,” “¬,” “≡,” “⊃” – for the logical operators. 1. Either existing home sales will decrease or new housing starts will increase and unemployment will decrease only if the Federal Reserve decreases long-term interest rates and foreign trade deficits decrease or foreign trade deficits increase and manufacturing rates increase. 2. Germany will vote to limit the number of immigrants it admits and so will reject Angela Merkel’s international policies unless neighboring EU countries agree to a multi-national work visa program and either the World Bank revalues the Euro relative to the US dollar or the US-Russia brokered peace treaty is signed by Syria.

Answer 1

P - existing home sales will decrease

Q - new housing starts will increase

R - unemployment will decrease

S - the Federal Reserve decreases long-term interest rates

T - foreign trade deficits decrease

U - foreign trade deficits increase

V - manufacturing rates increase

`[(P \vee Q) \wedge R] \iff (S \wedge T) \vee (U \wedge V)`

P - Germany will vote to limit the number of immigrants it admits

Q - will reject Angela Merkel’s international policies

R - neighboring EU countries agree to a multi-national work visa program

S - the World Bank revalues the Euro relative to the US dollar

T - the US-Russia brokered peace treaty is signed by Syria.

`\\eg (R \wedge (S \vee T))\implies (P \implies R)\\`