Question -
Answer -
Solution:
Yes, the statement “the product of twoconsecutive positive integers is divisible by 2” is true.
Justification:
Let the two consecutive positive integers = a,a + 1
According to Euclid’s division lemma,
We have,
a = bq + r, where 0 ≤ r < b
For b = 2, we have a = 2q + r, where 0 ≤ r< 2 … (i)
Substituting r = 0 in equation (i),
We get,
a = 2q, is divisible by 2.
a + 1 = 2q + 1, is not divisible by 2.
Substituting r = 1 in equation (i),
We get,
a = 2q + 1, is not divisible by 2.
a + 1 = 2q + 1+1 = 2q + 2, is divisible by 2.
Thus, we can conclude that, for 0 ≤ r < 2,one out of every two consecutive integers is divisible by 2. So, the product ofthe two consecutive positive numbers will also be even.
Hence, the statement “product of twoconsecutive positive integers is divisible by 2” is true.