Question

For each of the following statements, construct an open sentence P (x), P (x, y), or P (x, y, z), where x, y, z are variables, such that for some choice of values of the variables we obtain the original statement and for a different choice of values of the variables, it is possible to obtain a statement whose truth value is different than the original statement.

a. The square of 3 is larger than the cube of 2.
b. 4.3 + 8 = 30.
c. The population of Manitoba is larger than the population of Winnipeg.

Answer 1

a.)

Open statement : P(X,Y) = The square of X is larger than the cube of Y.

b.)

Open Statement : P(X,Y,Z) = X.Y + 8 = Z.

c.)

Open Statement : P(X,Y) = The population of X is larger than the population of Y.