# For a Gallup poll, #M# is the event of randomly selecting a male, and #R# is the event of randomly selecting a Republican. Are events #M# and #R# disjoint? Why or why not?

Those events are not disjoined. See explanation.

Two events are disjoined if and only if they cannot occur both at once.

Here the events are not disjoined because it is possible that the selected person is both a male and a Republican.

The possible disjoined events can be:

"selecting a Republican" and "selecting a Democrat".

In this example I assume there are no people who declare voting on two parties at once.

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Events M (randomly selecting a male) and R (randomly selecting a Republican) are not necessarily disjoint. Disjoint events are events that cannot occur simultaneously. In this case, it's possible for someone to be both male and a Republican. Therefore, events M and R are not necessarily disjoint. However, whether they are disjoint or not depends on the specific population being surveyed and the context of the poll.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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