Let S be a sample space for an experiment and let G and A be events of this experiment. Show that the events and are mutually exclusive.
Hint: Use De Morgan's law.

A) By De Morgan's law, , so the events are mutually exclusive.
B) By De Morgan's law, , so the events are mutually exclusive.
C) By De Morgan's law, , so the events are mutually exclusive.
D) By De Morgan's law, , so the events are mutually exclusive.
E) By De Morgan's law, , so the events are not mutually exclusive.

Question

Let S be a sample space for an experiment and let G and A be events of this experiment. Show that the events  and  are mutually exclusive. ​
Hint: Use De Morgan's law.
​
A) By De Morgan's law, , so the events are mutually exclusive. 
B) By De Morgan's law, , so the events are mutually exclusive. 
C) By De Morgan's law, , so the events are mutually exclusive. 
D) By De Morgan's law, , so the events are mutually exclusive. 
E) By De Morgan's law, , so the events are not mutually exclusive.

Quizplus · Accepted Answer

By De Morgan's law, the complement of G union A is equal to the complement of G intersect complement of A. Therefore, if the events G and A are mutually exclusive (i.e. they have no common outcomes), then their complements G^c and A^c must have outcomes in common. This means that G^c intersect A^c is non-empty. In this case, the complement of event 11eab448_e7c6_ed33_acdb_530a89fa849e_TB6027_11 is equal to event 11eab448_e7c6_ed35_acdb_3bd83e257e4c_TB6027_11, and the complement of event 11eab448_e7c6_ed34_acdb_db3febbaf014_TB6027_11 is equal to event 11eab448_e7c7_1446_acdb_1f606ead45c9_TB6027_11. Since these two events are complementary, they have no outcomes in common, and therefore the original events 11eab448_e7c6_ed33_acdb_530a89fa849e_TB6027_11 and 11eab448_e7c6_ed34_acdb_db3febbaf014_TB6027_11 are mutually exclusive.

Let S Be a Sample Space for an Experiment and Let