List Comprehensions

A list comprehension allows you to create lists quickly using syntax that looks like set-builder notation.

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a = [k*k for k in range(5)]
 
b = [k for k in range(13) if k%2 == 0]
 
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The list a contains the squares of 0 to 4 and b contains all even numbers from 0 to 12.

Sets and Set Operations

Sets are similar to lists, but they cannot have repeated entries and have special set operations.

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A = set([1,2,3,4,5])
 
B = set([3,4,5,6,7])
 
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(a)

We can determine the membership of an element x in a set A:

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x in A
      
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(b)

In the case of a finite set, we can compute its cardinality:

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len(A)
      
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(c)

We can determine if a set A is a subset of another set B:

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A.issubset(B)
      
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(d)

Unions:

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A.union(B)
      
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(e)

Intersection:

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A.intersection(B)
      
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(f)

Set Differences:

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A.difference(B)
      
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Problems

(a)

Use list comprehensions to create the following lists:

(i)

The list of all of the odd numbers from 1 to 100.

(ii)

The list of all letters in your name that are not ‘e’. (Hint: a string can be iterated over.)

(b)

Suppose $A=\{4,7,8,3,2\}$ and $B=\{8,7,5s,4\}$

(i)

Compute $A\cap B$.

(ii)

Compute $A\cup B$.

(iii)

Compute $A-B$.

(iv)

Compute $|A\cup B|$.