Let , , and be disjoint subsets of the sample space. For each one of the following statements, determine whether it is true or false. Note: "False" means "not guaranteed to be true."

a)

True FalseStatus: unsubmitted

b)

True FalseStatus: unsubmitted

c)

True FalseStatus: unsubmitted

d)

True FalseStatus: unsubmitted

Huh???

Speed is a measure of how fast something moves in a specific direction

To determine whether the given statements are true or false, we need to understand the definitions of disjoint subsets and the properties associated with them.

Disjoint subsets are sets that have no elements in common. In other words, if two subsets are disjoint, they do not share any elements.

a) The statement is true. If three subsets A, B, and C are disjoint, then the intersection of any two subsets is an empty set. So, A ∩ B = ∅, A ∩ C = ∅, and B ∩ C = ∅.

b) The statement is false. If three subsets A, B, and C are disjoint, it does not guarantee that their complements (Ac, Bc, and Cc) are disjoint as well. The complements of disjoint subsets can still have some overlap.

c) The statement is true. If three subsets A, B, and C are disjoint, then the union of all three subsets (A ∪ B ∪ C) is equal to the sum of their individual sizes (|A| + |B| + |C|). This property holds for any number of disjoint subsets.

d) The statement is false. If three subsets A, B, and C are disjoint, it does not guarantee that the intersection of their complements (Ac ∩ Bc ∩ Cc) is an empty set. The intersection of complements can still have some common elements.

So, the answers are:

a) True
b) False
c) True
d) False