Page 43 -

Algebra, Functions, Graphs, and Vectors 33

(x y)&(y z) → x z

(x y)&(y z) → x z

(x y)&(y z) → x z

(x y)&(y z) → x z

Additive inverses
For all real numberð x and y, the following statementð are log-
ically valid:

x y → x y

x y → x y

x y → x è y

x y → x è y

Reciprocals of positive reals
For all real numberð x and y where x 0 and y 0, the follow-
ing statementð are logically valid:

x y → 1/x 1/y

x y → 1/x 1/y

x y → 1/x 1/y

x y → 1/x 1/y

Reciprocals of negative reals
For all real numberð x and y where x 0 and y 0, the follow-
ing statementð are logically valid:

x y → 1/x 1/y

x y → 1/x 1/y

x y → 1/x 1/y

x y → 1/x 1/y