Question 1: For each of the following English phrases some candidate logical expressions are iven. For each one, say whether the logical expression (1) correctly expresses the English entence, (2) is syntactically invalid and therefore meaningless, or (3) is syntactically valid but loes not express the meaning of the English sentence. None of the examples below contain unctions; i.e. expressions like Country (c) are predications that mean " c is a country." a. Paris and Marseilles are both in France. (3 points) i. In(Paris Marseilles, France) ii. In( Paris, France )In( Marseilles, France ) iii. In(Paris, France) In (Marseilles, France) b. There is a country that borders both Iraq and Pakistan. (4 points) i. c Country (c)BBorder(c, Iraq )BBorder(c, Pakistan ) ii. c Country (c)( Border (c, Iraq )Border(c, Pakistan )) iii. (c Country (c))( Border (c, Iraq )Border(c, Pakistan )) iv. c Border ( Country (c), Iraq Pakistan) c. All countries that border Ecuador are in South America. (4 points) i. c Country (c) Border (c, Ecuador )In(c, SouthAmerica ) ii. c Country (c)( Border (c, Ecuador )In(c, SouthAmerica )) iii. c( Country (c) Border (c, Equador ))In(c, SouthAmerica ) iv. c Country (c) Border(c, Ecuador )In(c, SouthAmerica ) d. No region in South America borders any region in Europe. (4 points) i. (c,dIn(c, SouthAmerica )In(d, Europe )Borders(c,d)) ii. c,d(In(c, SouthAmerica )In(d, Europe ))Borders(c,d) iii. cIn(c, SouthAmerica )dIn(d, Europe )Borders(c,d) iv. cIn(c, SouthAmerica )dIn(d, Europe )BBorders(c,d) e. No two adjacent countries have the same color on a map. (4 points) i. x,yCountry(x)Country(y)Borders(x,y) (MapColor(x)=MapColor(y)) ii. x,y( Country (x)Country(y)Borders(x,y)(x=y)) (MapColor(x)=MapColor(y)) iii. x,y Country (x)Country(y)Borders(x,y) (MapColor(x)=MapColor(y)) iv. x,y(Country(x)Country(y)Borders(x,y))MapColor(x=y)