​If ‘a’ is an even positive integer and ‘b’ is an odd positive integer, then the true statement is:​

Correct option is C

Given:
​$$a = 2 \; (\text{even positive integer}), \\b = 3 \; (\text{odd positive integer}) \\[8pt]$$​​
Solution:
Option A: $$a(b-1)\text{ is odd} \\$$​​
​$$a(b-1) = 2(3-1) = 2 \times 2 = 4 \; (\text{even}) \\\Rightarrow \text{False} \\[8pt]$$​​
Option B: $$(a-1)(b-1)\text{ is odd} \\$$​​
​$$(a-1)(b-1) = (2-1)(3-1) = 1 \times 2 = 2 \; (\text{even}) \\\Rightarrow \text{False} \\[8pt]$$​​
Option C: $$a(b-1)\text{ is even} \\$$​​
​$$a(b-1) = 4 \; (\text{even}) \\\Rightarrow \text{True} \\[8pt]$$​​
Option D: $$(a+1)(b+1)\text{ is odd} \\$$​​
​$$(a+1)(b+1) = (2+1)(3+1) = 3 \times 4 = 12 \; (\text{even}) \\\Rightarrow \text{False} \\[12pt]$$​​
Correct answer is (C) $$a(b-1)\text{ is even}$$​​