Answer:
There are 4 questions to answer here and the answers are given below:
1. COMBINATION
2. SET 2
3. {S2, S3, S4, S5}
4. { } OR ∅
Step-by-step explanation:
The key topics here are PERMUTATION & COMBINATION and SETS & VENN DIAGRAMS.
The assignment has 5 questions in all. The options for each question are listed below and separated by commas:
1. True, False
2. True, False
3. A, B, C, D
4. A, B, C, D
5. A, B, C, D
Mr. Montes derives his answers from a random answer generator; same way Amisha generated her answers by random selection.
<u>QUESTION 1</u>
If you want to find the odds that Amisha got at least 3/5 of the answers correctly, would you use a permutation or a combination?
<u>ANSWER TO QUESTION 1</u>
You would use a combination. Note that as much as 'permutation' is distinctly defined from 'combination', in many complex cases both are used to derive the solution. In this case though, a combination is used. For each of the 5 questions, there are a number of possible answers. Questions 1 and 2 have only <em>two possible answers</em> (also known as options) while questions 3, 4 and 5 have <em>four possible answers</em>/<em>options</em> to choose from. Amisha can only have one set of five answers; each to each question. So this is a combination! If you want to find the odds that Amisha got at least 3 of her 5 answers correct, you would use a combination of the various possible answers to check.
<u>QUESTION 2</u>
Find "Set 1 ∩ Set 2" and explain the notation in the sentence.
<u>ANSWER TO QUESTION 2</u>
First list out relevant information:
- The correct answers to questions 3, 4 and 5 are respectively C, B, A
- The universal set consists of five students: S1, S2, S3, S4, S5 hence
Ц = {S1, S2, S3, S4, S5}
Next, enlist the elements of each defined set
Set 1: {S1, S2, S3, S4, S5} Set 2: {S2, S3, S4} Set 3: {S4, S5}
Note: Set 1 is equal to the universal set.
Now this notation "∩" means "intersect". It requires an action - checking out which elements in one set also appear in a second set and then bringing those elements to form a new set.
In the case of this question, we're to find Set 1 intersect Set 2. The elements present in Set 1 and also present in Set 2 are {S2, S3, S4}.
If you look closely, you'll observe that these are the same elements in Set 2! This brings to remembrance, one of the laws of sets:
The intersect of any subset and the universal set (recall that Set 1 happens to be equal to or have the same elements as the universal set) is equal to that subset.
So the answer to question 2 is
Set 1 ∩ Set 2 = Set 2
<u>QUESTION 3</u>
Find "Set 2 ∪ Set 3" and explain the notation in the sentence.
<u>ANSWER TO QUESTION 3</u>
The notation ∪ represents "union". This is the act of putting together the elements in two sets, to form a new set. In this activity, if an element appears in both sets, it is only written once in the new set, not twice.
So, Set 2 union Set 3 = {S2, S3, S4, S5}
As earlier stated, Student 4 isn't appearing twice in the new set.
<u>QUESTION 4</u>
Find the ' of Set 1 and explain the notation in this sentence.
<u>ANSWER TO QUESTION 4</u>
The symbol ' means "complement of a set". Finding the complement of a set is like subtracting the elements of that set from the universal set.
Since Set 1 contains the same elements as the universal set, subtracting Set 1 from the universal set will give you nothing. In this case, the complement of Set 1 is a null set!
Set 1 ' Ц = { } or ∅
where the empty bracket symbol and the slashed zero symbol represent null set.
Kudos!