Induction proof: Prove that |{x subset of A | |x| = 2}| = n(n-1)2

[sita]

Let A be a set of size n, where n is an integer. Prove by induction that |{x ⊆ A | |x| = 2}| =n(n−1)2

Sub in value of p(n)

induction part (n+1)

Not sure how to apply further info such as induction hypothesis please help.

 

[stapel]

Let A be a set of size n, where n is an integer. Prove by induction that |{x ⊆ A | |x| = 2}| =n(n−1)2

Is the "2" that follows "n(n-1)" meant to be a multiplier, as written? Or is it meant to be a power, so the "(n-1)" is squared?

Also, is it correct to read the "prove" statement as follows?

"Let A be a set, and let X be a subset of A having a cardinality of 2. Prove that, when the cardinality of A is n > 2, the cardinality of the set of all such subsets X is equal to n (n – 1)²."

Sub in value of p(n)

I'm sorry, but I don't know what this means...? Does "sub in" indicate "substitute" something into something else? If so, what went into what? What is the meaning of "p(n)"?

induction part (n+1)

What does this mean? Are you saying that you've done something or other with the "now let n = k + 1" portion of the exercise? If so, what did you do? (Please show your work.) If not, please explain what this indicates.

Please be complete. Thank you!

 

[sita]

Is the "2" that follows "n(n-1)" meant to be a multiplier, as written? Or is it meant to be a power, so the "(n-1)" is squared?

Also, is it correct to read the "prove" statement as follows?

"Let A be a set, and let X be a subset of A having a cardinality of 2. Prove that, when the cardinality of A is n > 2, the cardinality of the set of all such subsets X is equal to n (n – 1)²."


I'm sorry, but I don't know what this means...? Does "sub in" indicate "substitute" something into something else? If so, what went into what? What is the meaning of "p(n)"?


What does this mean? Are you saying that you've done something or other with the "now let n = k + 1" portion of the exercise? If so, what did you do? (Please show your work.) If not, please explain what this indicates.

Please be complete. Thank you!

Its a divider

Sub as in subsititute

 

[sita]

Is the "2" that follows "n(n-1)" meant to be a multiplier, as written? Or is it meant to be a power, so the "(n-1)" is squared?

Also, is it correct to read the "prove" statement as follows?

"Let A be a set, and let X be a subset of A having a cardinality of 2. Prove that, when the cardinality of A is n > 2, the cardinality of the set of all such subsets X is equal to n (n – 1)²."


I'm sorry, but I don't know what this means...? Does "sub in" indicate "substitute" something into something else? If so, what went into what? What is the meaning of "p(n)"?


What does this mean? Are you saying that you've done something or other with the "now let n = k + 1" portion of the exercise? If so, what did you do? (Please show your work.) If not, please explain what this indicates.

Please be complete. Thank you!

It's meant to be divide by 2

and Substitute

 

[stapel]

It's meant to be divide by 2

So the actual exercise is more like the following?

"Let A be a set, and let X be a subset of A having a cardinality of 2. Prove that, when the cardinality of A is n > 2, the cardinality of the set of all such subsets X is equal to \(\displaystyle \dfrac{n\, (n\, -\, 1)}{2}.\)"

and Substitute

So you substituted (something, but what?) into (something else, but what?) at (some stage, but where?) of your working (which is what?)...?

Please reply with a clear listing of your steps so far, so we can see what's going on. Since we cannot read your mind, it would be helpful if you spoke in complete sentences using standard English. If you are translating from another language, kindly please find a friend with better familiarity with English, to help you clarify what you're doing and asking. Thank you!