Let the set values be,

S = {-10, -6, -2, 0, 1, 5, 8, 10, 100}

T = (-6, -2, 0, 1, 5, 8, 10, 100}

What is the solution for this?

@gregmat

Let the set values be,

S = {-10, -6, -2, 0, 1, 5, 8, 10, 100}

T = (-6, -2, 0, 1, 5, 8, 10, 100}

What is the solution for this?

@gregmat

why donâ€™t you solve it and then we can infer at what step youâ€™re making the mistake

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Yep, I did. For this mentioned set all the mentioned option choices are hold false. But in the video, it was mentioned as option E as answer. I am bit confused on how to approach it?

Can you show how you did it? It is always recommend to post your solution so that other can point how where exactly (at which step) youâ€™re going wrong. I can put a full solution for you but that way youâ€™ll learn nothing because youâ€™ll try to copy my way of thinking!

Anyways, here is how I solve it with your values:

The smallest element of S is `-10`

and the largest element of S is `100`

. Therefore, the range of S is `range(S) = max(S) - min(S) = 100 - (-10) = 110`

.

The smallest element of T is -6 and the largest element of T is 100. Therefore, the range of T is `range(T) = max(T) - min(T) = 100 - (-6) = 106`

.

Since `range(S) = 110`

and `range(T) = 106`

, we can see that the range of S is greater than the range of T. Therefore, statement E cannot be true for these values of S and T.

T is a subset of S. This means that all elements of T are also elements of S. Therefore, the smallest element of T must be greater than or equal to the smallest element of S, and the largest element of T must be less than or equal to the largest element of S.

**Logical way**:

Letâ€™s denote the smallest element of S as `min(S)`

and the largest element of S as `max(S)`

. Similarly, letâ€™s denote the smallest element of T as `min(T)`

and the largest element of T as `max(T)`

. Since T is a subset of S, we have `min(S) <= min(T)`

and `max(S) >= max(T)`

.

Now letâ€™s consider the range of S and T. The range of S is `range(S) = max(S) - min(S)`

and the range of T is `range(T) = max(T) - min(T)`

. Since `max(S) >= max(T)`

and `min(S) <= min(T)`

, we have `range(S) = max(S) - min(S) >= max(T) - min(T) = range(T)`

.

Therefore, it is not possible for the range of S to be less than the range of T. So statement E cannot be true.

Yep the below is my solution for the problem. BTW You didnâ€™t solve the question! You solved only for the Option E!

A. Mean:

s = 11.77

T = 14.5

Mean(S) NOT EQUAL TO Mean of (T)

This statement can not be true

B. Median:

S = 1

T = 3

Median(S) NOT EQUAL TO Median(T)

This statement can not be true

C. Range:

S = 110

T = 106

Range(S) NOT EQUAL TO Range(T)

This statement can not be true

D. Mean:

s = 11.77

T = 14.5

Mean(S) LESS THAN Mean of (T)

This statement can not be true

E. Range:

S = 110

T = 106

Range(S) GREATER THAN Range(T)

This statement can not be true

This is the way I solved the question. So I guess from this you can infer all the statements are false, in such case how to determine the answer.

Because question asked `cannot be True`

, expect for E , all other can be True for some cases; hence, I just showed which was correct choice ; but here is example of cases when other are True:

A. The mean of S is equal to the mean of T: This can be true if the number that is in set S but not in set T is equal to the mean of set T. For example, let S = {1, 2, 3, 4} and T = {1, 2, 3}. The mean of T is (1 + 2 + 3) / 3 = 2. Since the number that is in S but not in T is also 2, the mean of S is also (1 + 2 + 2 + 3) / 4 = 2.

B. The median of S is equal to the median of T: This can be true if the number that is in set S but not in set T is either greater than or less than all the numbers in set T. For example, let S = {1, 2, 3, 4} and T = {1, 2, 3}. The median of T is 2. Since the number that is in S but not in T (4) is greater than all the numbers in T, the median of S is also 2.

C. The range of S is equal to the range of T: This can be true if the number that is in set S but not in set T is either greater than or less than all the numbers in set T. For example, let S = {1, 2, 3, 4} and T = {1, 2, 3}. The range of T is (3 - 1) = 2. Since the number that is in S but not in T (4) is greater than all the numbers in T, the range of S is also (4 - 1) = 3.

D. The mean of S is greater than the mean of T: This can be true if the number that is in set S but not in set T is greater than the mean of set T. For example, let S = {1, 2, 3, 4} and T = {1, 2, 3}. The mean of T is (1 + 2 + 3) / 3 = 2. Since the number that is in S but not in T (4) is greater than the mean of T (2), the mean of S ( (1 + 2 + 3 +4) /4 )is greater than the mean of T.

You can even take S = {1,2} and T = {1} and then can just work it out very fast ; the S = 9 element and T = 8 element is a **TRAP** to waste your time

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