For each of the following mathematical expressions involving set notation presen

Question

For each of the following mathematical expressions involving set notation presented in the Mathematical Set Notation slides, provide the value of the expression.

12 is in { 41, 23, -35, 8 }

23 is not in { 41, 23, -35, 8 }

{ } union { 'x', 'y', 'z' }

{ 'x', 'y', 'z' } union { 'x', 'y', 'w' }

{ 'x', 'y', 'z' } intersection { 'x', 'y', 'w' }

{ 'x', 'y', 'z' } intersection { }

{ 'x', 'y', 'z' } { 'x', 'y', 'w' }

{ } { 'x', 'y', 'z' }

{ 1, 2, 3 } is subset of { 2, -2, 3, 1, 7 }

{ 1, 2, 3 } is proper subset of { 1, 2, 3}

|{ 'x', 'y', 'z' }|

entries(< 'b', 'a', 'b', 'c', 'b' >)

Given the following fragments, reassemble the original string by applying the greedy reassembly algorithm presented in the Genome/String Reassembly slides. Show in each step the two strings with the longest overlap and the resulting combination.

TATACAT

AGCTGTTTTCGTT

CACTCCATTTTA

CATTTTAGCTGTT

TTTCGTTATACAT

CTGTTTTCGTTA

Implement the instance method flip declared as follows (this is a Queue<T>):

/**

* Reverses ("flips") {@code this}.

*

* @updates this

* @ensures this = rev(#this)

*/

public void flip();

Rewrite flip, including the contract, so that it is a static method.

/**

* Reverses ("flips") {@code this}.

*

* @updates this

* @ensures this = rev(#this)

*/

public void flip();

Explanation / Answer

12 is in { 41, 23, -35, 8 } is false

23 is not in { 41, 23, -35, 8 } is false

{ } union { 'x', 'y', 'z' } is { 'x', 'y', 'z' }

{ 'x', 'y', 'z' } union { 'x', 'y', 'w' }  is { 'x', 'y', 'z','w' }

{ 'x', 'y', 'z' } intersection { 'x', 'y', 'w' } is { 'x', 'y' }

{ 'x', 'y', 'z' } intersection { } is { }

{ 'x', 'y', 'z' } { 'x', 'y', 'w' } is { 'z' }

{ } { 'x', 'y', 'z' } is { }

{ 1, 2, 3 } is subset of { 2, -2, 3, 1, 7 } is true

{ 1, 2, 3 } is proper subset of { 1, 2, 3 } is false

|{ 'x', 'y', 'z' }| is 3

entries(< 'b', 'a', 'b', 'c', 'b' >) is undefined

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