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Given that π΄ and π΅ are two events in a sample space of a random experiment, where π΅ β π΄, determine π΅ β π΄.

Given that π΄ and π΅ are two events in a sample space of a random experiment, where π΅ is a subset of π΄, determine π΅ minus π΄.

The notation π΅ minus π΄ denotes the difference of two events. In general, we say that π΅ minus π΄ is the set of elements π₯ that occur in event π΅ and do not occur in event π΄. In this question, we are told that π΅ is a subset of π΄. Letβs consider what this looks like on a Venn diagram. If π΅ is a subset of π΄ as in this case, then every element of π΅ is also in π΄. The entire circle representing the elements in event π΅ is contained in the circle representing the elements in event π΄.

It is clear from the definition and the diagram that there are no elements of event π΅ that are not in event π΄. This means that if π΅ is a subset of π΄, then π΅ minus π΄ is the empty set.

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