Even and odd integer operations – UGC NET Question

Statement B is true because adding an odd and an even number always yields an odd result. C is correct since the product of two odd numbers is odd. D is also correct because an odd times an even number always has a factor 2 and so is even. A is false because the sum of two odd integers is even, and E is false because not every even number is divisible by 3. Hence B, C and D only are correct.

Option A:
Option A is incomplete as it leaves out D and therefore does not include the important rule about the product of an odd and even number, which is regularly tested in parity questions.

Option B:
Option B is correct because it gathers all three standard parity rules, covering sums and products of odd and even numbers, while excluding A and E, which misstate these relationships.

Option C:
Option C is incorrect since it includes A, which wrongly claims that two odd numbers add to an odd result, contradicting parity arithmetic.

Option D:
Option D is wrong as it brings in E, which incorrectly generalises divisibility by 3 to all even numbers, and so mixes a false divisibility statement with otherwise correct parity rules.