Chapter 12.5, Problem 1E

Determine whether each statement is true or false in ${ℝ}^3$.

(a) Two lines parallel to a third line are parallel.

(b) Two lines perpendicular to a third line are parallel.

(c) Two planes parallel to a third plane are parallel.

(d) Two planes perpendicular to a third plane are parallel.

(e) Two lines parallel to a plane are parallel.

(f) Two lines perpendicular to a plane are parallel.

(g) Two planes parallel to a line are parallel.

(h) Two planes perpendicular to a line are parallel.

(i) Two planes either intersect or are parallel.

(j) Two lines either intersect or are parallel.

(k) A plane and a line either intersect or are parallel.