Computer Sciences > GATE 2023 > Discrete Mathematics
Let f: A → B be an onto (or surjective) function, where A and B are nonempty sets. Define an equivalence relation ~ on the set A as
a1 ~ a2 if f(a1) = f(a2),
where a1, a2 ∈ A. Let E = {[x]: x ∈ A} be the set of all the equivalence classes under ~. Define a new mapping F: E → B as
F([x]) = f(x), for all the equivalence classes [x] in E.
Which of the following statements is/are TRUE?
a1 ~ a2 if f(a1) = f(a2),
where a1, a2 ∈ A. Let E = {[x]: x ∈ A} be the set of all the equivalence classes under ~. Define a new mapping F: E → B as
F([x]) = f(x), for all the equivalence classes [x] in E.
Which of the following statements is/are TRUE?
Explanation
Correct : b,c,d
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