Set Theory, Calendars, Clocks and Binomial Theorem

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Set Theory - De Morgan's Laws

    A´ is defined as the complement of A, as in, set of all elements that are part of the universal set but not in A. How many of the following have to be true?

    i.
    ii. If , then is equal to the universal set
    iii. If = universal set, then should be the null set.
    iv. If then
    1. 1
    2. 2
    3. 3
    4. 4

 

  • Correct Answer
    Choice D. all four statements are true.

Explanatory Answer

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Detailed Solution

Let's look at these statements one at a time:

i.
This is a direct statement of De Morgan´s law. This is definitely true. Just to recap, De Morgan´s laws are as follows:
1.
2.

ii. , then is equal to the universal set


If A and B are disjoint sets, and is the universal set. This statement is correct.

iii. If = Universal Set, then should be the null set. This means is the null set.

iv. If , then

If then .
This implies that

If , then and

Thus . This statement is true.

Correct Answer: All four statements are true.



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