Question

Construct a translation of the given compound statement into propositional logic notation.

Statement:
California's having a gold rush is a sufficient condition for its being admitted into the Union; moreover, Alaska's having gold rush and Its being purchased from Russia is sufficient condition for its being admitted into the Union and its having two senators.

A =Alaska has a gold rush.
C= California has a gold rush.
L= California is admitted into the union.
R =Alaska is purchased from Russia.
S = Alaska has two senators.
U = Alaska is admitted into the Union.

Answer 1

Step-by-step explanation:

This is how we translate the statement that is contained in this question into logic.

(C→L)^[(A^R) →(U^S)]

Each of these alphabets above stands for the statements that we have in the question.

CThis is how we translate the statement that is contained in this question into logic.

(C→L)^[(A^R) →(U^S)]

Each of these alphabets above stands for the statements that we have in the question.

C→L shows california fulfilled condition for it to be a part of the union

[(A^R) →(U^S)] shows that there is a gold rush in Alaska in conjunction to the fact that Russia has purchased, now alaska is part of the union because they have 2 senators.

^ shows conjunction

→ shows implication