1) Find a bijection from R to R N, where N denotes the set of all natural numbers. 2) Is there an injection from R into Q, the set of all rational

1) Find a bijection from R to R − N, where N denotes the set of all natural numbers.2) Is there an injection from R into Q, the set of all rational numbers? Why?Please be specific.

SOLUTIONS1) A function f: R R­N, given by f(x) = ­x is a bijection from R toR­N. As, this is both injective (One-to-one) function and surjective (Onto) function. Here, image of distinct…