Tarski’s World: Part 2
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For each of the statements on the following page, write the statement in formal logical
notation and then determine whether it is true or false. Then write the negation of each
statement in formal logical notation. The domain for each statement is the set of objects in
the Tarski world shown above.
Recall Tarski World notation:
Notation
Meaning
Triangle(x)
x is a triangle
Square(x)
x is a square
Circle(x)
x is a circle
Rightof(x,y)
x is to the right of y
Above(x,y)
x is above y
SameColor(x,y) x is the same color as y
(1) There is a triangle x such that for all squares y, x is above y.
NOTATION:
TRUE
or
FALSE
NEGATION:
(2) For all circles x, there is a square y such that y is to the right of x.
NOTATION:
TRUE
or
FALSE
NEGATION:
(3) There is an object y such that for all objects x, if x 6= y then x and y have different
colors.
NOTATION:
TRUE
or
FALSE
NEGATION:
(4) There is a circle x and there is a square y such that x and y have the same color.
NOTATION:
TRUE
NEGATION:
or
FALSE