Description
Problems. Inside the file pa2.py place functions as described below which solve each of the
following problems. Only include these three functions, and be sure to title them as described in
the problems. (Improperly titled functions will not be called properly.) To write these functions,
it should be sufficient to understand the documents on Logic and on Tuples and Sets listed on the
course programming page.
1. Write a function named implies(P,Q) that takes as input two boolean values P and Q and
returns the truth value of the statement “P implies Q.” (You can test your function using the
print_truth_table function given on the Logic page.)
2. Write a function named iff(P,Q) that takes as input two boolean values P and Q and returns
the truth value of the statement “P iff Q.”
3. Say that a 2-input truth function is a function which takes as input two boolean values P and
Q and returns a boolean value.( Examples include xor above, as well as implies and iff from the
problems above.)
Write a function named logically_equivalent(tf1, tf2) that takes as input two 2-input
truth functions tf1 and tf2 and returns the boolean value of the statement ”The two truth
functions are logically equivalent.” Your function should return True if and only if the two
functions tf1 and tf2 return the same output whenever they are passed the same input values.
Examples of successful input/output:
>>> def or_not(P,Q):
return (not P) or (not Q)
>>> def not_and(P,Q):
return not (P and Q)
>>> logically_equivalent(or_not, not_and)
True
>>> def or_function(P,Q):
return P or Q
>>> logically_equivalent(or_function, not_and)
False
4. Write a function planar_distance(p,q) which takes as input two points in the plane and
returns the distance between them. Here a point in the plane should be interpreted as a 2-tuple
whose entries are both real numbers.
Examples of successful input/output:
>>> print(planar_distance( (0,0), (1,1) ))
1.4142135623730951
>>> print(planar_distance( (1,1), (4,5) ))
5.0
5. Suppose A and B are two sets of numbers. Their sumset is the set
{a + b : a ∈ A and b ∈ B}.
Write a function called sumset(A,B) which takes as input two sets of numbers A and B and
returns their sumset.
Examples of successful input/output:
>>> sumset({1,2,3},{1,2,3})
{2, 3, 4, 5, 6}
>>> sumset({-1,1},{3,10})
{9, 2, 11, 4}