Answer:
Let P(x) = x is in the correct place
Let Q(x) = x is in the excellent place
R(x) denotes the tool
Explanation:
a) Something is not in the correct place.
P(x) is that x is in the correct place so negation of ¬P(x) will represent x is not in the correct place. ∃x is an existential quantifier used to represent "for some" and depicts something in the given statement. This statement can be translated into logical expression as follows:
∃x¬P(x)
b) All tools are in the correct place and are in excellent condition.
R(x) represents the tool, P(x) represents x is in correct place and Q(x) shows x is in excellent place. ∀ is used to show that "all" tools and ∧ is used here because tools are in correct place AND are in excellent condition so it depicts both P(x) and Q(x). This statement can be translated into logical expression as follows:
∀ x ( R(x) → (P(x) ∧ Q(x))
c) Everything is in the correct place and in excellent condition.
Here P(x) represents correct place and Q(x) represents excellent condition ∀ represent all and here everything. ∧ means that both the P(x) and Q(x) exist. This statement can be translated into logical expression as follows:
∀ x (P(x) ∧ Q(x)
No one could possibly know, unfortunately.
Answer:
// program in Python to check perfect number
#function to find number is perfect or not
def is_Perfect_Number(n):
#total variable
tot = 1
i = 2
#sum of all divisor of number
while i*i<=n:
if n%i==0:
tot = tot + i + n/i
if tot == n and n != 1:
return 1
i = i+1
return 0
#read until user enter a perfect number
while True:
#read integer
num = int(input("Input an integer: "))
#call the function
if(is_Perfect_Number(num)):
print(num,"is perfect number")
#if perfect number break
break
else:
print(num,"is not a perfect number")
#ask again
print("try again.")
Explanation:
Read number from user and then call the function is_Perfect_Number() with parameter "num".This will find the sum of all divisor of number.If sum is equal to number then it will return 1 else return 0.If the number is not perfect then it will again ask to enter a number until user enter a perfect number.
Output:
Input an integer: 24
24 is not a perfect number
try again.
Input an integer: 28
28 is perfect number
