Answer:
The value of r can only be even if both value of P and q are even
Exploring the 3 possible scenarios:
If p is even and q is odd:
the value of Pq is even and P ₊ q is odd
Hence, the value of r (r = pq + p + q) is : even number ₊ odd number = odd number
e.g if p=2 and q=3
r = pq + p + q = 2*3 + 2+3 =6 +5 =11
and If p is odd and q is odd:
the value of Pq is odd and P ₊ q is even
Hence, the value of r (r = pq + p + q) is : odd number ₊ even number= odd number
e.g if p=5 and q=3
r = pq + p + q = 5*3 + 5+3 =15 + 8 = 23
If p is even and q is even:
the value of Pq is even and P ₊ q is even
Hence, the value of r (r = pq + p + q) is : even number ₊ even number= even number
e.g if p=2 and q=4
r = pq + p + q = 2*4 + 2+4 =8 + 6= 14
