For some integer 𝑞, every odd integer can be written in the form:

We know that, Odd integers like 1, 3, 5, 7,....are not divisible by 2 And even integers like 2, 4, 6, 8,.....are multiples of 2. 

So they are of the form 2𝑞 where 𝑞 is some integer. When we add '1' to 2𝑞 we get 2𝑞 + 1 2𝑞 + 1 is an odd integer form.

Hence for some integer 𝑞, every odd integer is of the form 2𝑞 + 1 

Hence option (𝑑) 2𝑞 + 1 is correct.