If cardinality of setA is less than cardinality of set B then.
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Answer:A natural choice for an injection is the function f(x) = {x}, which in plain English, takes any element x (that is in A) and sends it to the one-element set {x}. Thus f(x) is injective!
To show that there is no surjection, for the sake of contradiction, assume there is a surjection. Here is where I start to have trouble. Surjectivity means that every element of the co-domain is mapped to an element of the domain, correct? Consequently, in this particular case, we are "matching" sets (from P(A)) to elements (from A) right?
If the above is correct, my problem arises here. I am not sure how to prove that f is not surjective. Unfortunately, I am easily confused by notation so please explain in English. Thank you in advance!! :)
Step-by-step explanation: