Translate the following ordinary-language sentences into logical symbolic form u

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.

2.Germany will vote to limit the number of immigrants it admits and so will reject Angela Merkel’s international policies unless neighbouring 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.

Explanation / Answer

The " • " symbolizes logical conjunction; a compound statement formed with this connective is true only if both of the component statements between which it occurs are true. Whenever either of the conjuncts (or both) is false, the whole conjunction is false.

The symbol " " signifies inclusive disjunction: a   statement is true whenever either (or both) of its component statements is true; it is false only when both of them are false

The    symbol is used to symbolize a relationship called material implication; a compound statement formed with this connective is true unless the component on the left is true and the component on the right is false

Finally, the    is used to symbolize material equivalence, in which the compound statement is true only when its component statements have the same truth-value—either both are true or both are false.

The " ~ " signifies logical negation; it simply reverses the truth value of any statement in front of which it appears: if the original is true, the  ~ statement is false, and if the original is false, the  ~ statement is true

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