Question

Determine whether the sets have a subset relationship. R = {right triangles} O = {obtuse triangles} a) R and O are disjoint. B) R and O are equivalent. C) Subset of R and O is all triangles. D) Subset of R and O is all acute triangles. E) Subset of R and O is all triangles with two acute angles f) None of the above

Answer 1

Answer: Choice A

Reason:

If one of the angles is 90 degrees, then 180-90 = 90 is the sum of the other two angles. Neither of the other two angles can be obtuse, which rules out the possibility of an obtuse angle.

Therefore, if a triangle is a right triangle, then it cannot be obtuse, and vice versa.

In other words, if you are in set R, then you cannot be in set O, and vice versa.

The set R and set O have no overlap. The intersection of these sets is the empty set. We consider the sets disjoint.

Another example of disjoint sets would be P = {4,5,6} and Q = {7,8,9} since they have nothing in common.