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Propositional logic with itertools

Nov 18, 2022AustinLeath

0 likes • 5 views

from itertools import product
V='∀'
E='∃'
def tt(f,n) :
xss=product((0,1),repeat=n)
print('function:',f.__name__)
for xs in xss : print(*xs,':',int(f(*xs)))
print('')
# p \/ (q /\ r) = (p \/ q) /\ (p \/ r)
def prob1(p,q,r) :
x=p or (q and r)
y= (p or q) and (p or r)
return x==y
tt(prob1,3)
# p/\(q\/r)=(p/\q)\/(p/\r)
def prob2(p,q,r) :
x=p and ( q or r )
y=(p and q) or (p and r)
return x==y
tt(prob2,3)
#~(p/\q)=(~p\/~q)
def prob3(p,q) :
x=not (p and q)
y=(not p) or (not q)
return x==y
tt(prob3,2)
#(~(p\/q))=((~p)/\~q)
def prob4(p, q):
x = not(p or q)
y = not p and not q
return x == y
tt(prob4, 2)
#(p/\(p=>q)=>q)
def prob5(p,q):
x= p and ( not p or q)
return not x or q
tt(prob5,2)
# (p=>q)=((p\/q)=q)
def prob6(p,q) :
x = (not p or q)
y=((p or q) == q)
return x==y
tt(prob6,2)
#((p=>q)=(p\/q))=q
def prob7(p,q):
if ((not p or q)==(p or q))==q:
return 1
tt(prob7,2)
#(p=>q)=((p/\q)=p)
def prob8(p,q):
if (not p or q)==((p and q)==p):
return 1
tt(prob8,2)
#((p=>q)=(p/\q))=p
def prob9(p,q):
if ((not p or q)==(p and q))==p:
return '1'
tt(prob9,2)
#(p=>q)/\(q=>r)=>(p=>r)
def prob10(p,q,r) :
x = not ((not p or q) and (not q or r)) or (not p or r)
return x
tt(prob10, 3)
# (p = q) /\ (q => r) => (p => r)
#answer 1
def prob11(p,q,r) :
x = not((p is q) and (not q or r)) or (not p or r)
return x
tt(prob11, 3)
#(p=q)/\(q=>r)=>(p=>r)
#answer 2
def prob11(p,q,r):
x=(p==q) and (not q or r)
y=not p or r
return not x or y
tt(prob11,3)
#((p=>q)/\(q=r))=>(p=>r)
def prob12(p,q,r):
x=(not p or q) and ( q==r )
y=not p or r
return not x or y
tt(prob12,3)
#(p=>q)=>((p/\r)=>(q/\r))
def prob13(p,q,r):
x=not p or q
y=(not(p and r) or ( q and r))
return not x or y
tt(prob13,3)
#Question#2----------------------------------------
#(p=>q)=>r=p=>(q=>r)
def prob14(p,q,r):
x=(not(not p or q) or r)
y=(not p or (not q or r))
return x==y
tt(prob14,3)
def prob15(p, q):
x = not(p and q)
y = not p and not q
return x == y
tt(prob15, 2)
def prob16(p, q):
x = not(p or q)
y = not p or not q
return x == y
tt(prob16, 2)
def prob17(p):
x = p
y = not p
return x == y
tt(prob17, 1)

Using logic with sets

Nov 18, 2022AustinLeath

0 likes • 1 view

#Sets
U = {0,1,2,3,4,5,6,7,8,9}
P = {1,2,3,4}
Q = {4,5,6}
R = {3,4,6,8,9}
def set2bits(xs,us) :
bs=[]
for x in us :
if x in xs :
bs.append(1)
else:
bs.append(0)
assert len(us) == len(bs)
return bs
def union(set1,set2) :
finalSet = set()
bitList1 = set2bits(set1, U)
bitList2 = set2bits(set2, U)
for i in range(len(U)) :
if(bitList1[i] or bitList2[i]) :
finalSet.add(i)
return finalSet
def intersection(set1,set2) :
finalSet = set()
bitList1 = set2bits(set1, U)
bitList2 = set2bits(set2, U)
for i in range(len(U)) :
if(bitList1[i] and bitList2[i]) :
finalSet.add(i)
return finalSet
def compliment(set1) :
finalSet = set()
bitList = set2bits(set1, U)
for i in range(len(U)) :
if(not bitList[i]) :
finalSet.add(i)
return finalSet
def implication(a,b):
return union(compliment(a), b)
###########################################################################################
###################### Problems 1-6 #######################################
###########################################################################################
#p \/ (q /\ r) = (p \/ q) /\ (p \/ r)
def prob1():
return union(P, intersection(Q,R)) == intersection(union(P,Q), union(P,R))
#p /\ (q \/ r) = (p /\ q) \/ (p /\ r)
def prob2():
return intersection(P, union(Q,R)) == union(intersection(P,Q), intersection(P,R))
#~(p /\ q) = ~p \/ ~q
def prob3():
return compliment(intersection(P,R)) == union(compliment(P), compliment(R))
#~(p \/ q) = ~p /\ ~q
def prob4():
return compliment(union(P,Q)) == intersection(compliment(P), compliment(Q))
#(p=>q) = (~q => ~p)
def prob5():
return implication(P,Q) == implication(compliment(Q), compliment(P))
#(p => q) /\ (q => r) => (p => r)
def prob6():
return implication(intersection(implication(P,Q), implication(Q,R)), implication(P,R))
print("Problem 1: ", prob1())
print("Problem 2: ", prob2())
print("Problem 3: ", prob3())
print("Problem 4: ", prob4())
print("Problem 5: ", prob5())
print("Problem 6: ", prob6())
'''
Problem 1: True
Problem 2: True
Problem 3: True
Problem 4: True
Problem 5: True
Problem 6: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
'''

Differentiate Between type() and instance()

May 31, 2023CodeCatch

0 likes • 0 views

class Rectangle:
pass
class Square(Rectangle):
pass
rectangle = Rectangle()
square = Square()
print(isinstance(rectangle, Rectangle)) # True
print(isinstance(square, Rectangle)) # True
print(isinstance(square, Square)) # True
print(isinstance(rectangle, Square)) # False
my_list = [1, 2, 3, 4, 5]
removed_element = my_list.pop(2) # Remove and return element at index 2
print(removed_element) # 3
print(my_list) # [1, 2, 4, 5]
last_element = my_list.pop() # Remove and return the last element
print(last_element) # 5
print(my_list) # [1, 2, 4]

delay time lambda

Nov 19, 2022CodeCatch

0 likes • 0 views

from time import sleep
def delay(fn, ms, *args):
sleep(ms / 1000)
return fn(*args)
delay(lambda x: print(x), 1000, 'later') # prints 'later' after one second

Remove i'th character

Nov 19, 2022CodeCatch

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# Python code to demonstrate
# method to remove i'th character
# Naive Method
# Initializing String
test_str = "CodeCatch"
# Printing original string
print ("The original string is : " + test_str)
# Removing char at pos 3
# using loop
new_str = ""
for i in range(len(test_str)):
if i != 2:
new_str = new_str + test_str[i]
# Printing string after removal
print ("The string after removal of i'th character : " + new_str)