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?
Correct : b,c,d
Similar Questions
The Lucas sequence Ln is defined by the recurrence relation: Ln = Ln-1 + Ln-2, for n ≥ 3, with L1 = 1 and L2 = 3. Which one of the options given is TRUE?
Geetha has a conjecture about integers, which is of the form ∀x(P(x)⇒∃yQ(x,y)), where P is a statement about integers, and Q is a statement about pairs of integ...
Let U = {1, 2,...,n}, where n is a large positive integer greater than 1000. Let k be a positive integer less than n. Let A, B be subsets of U with |A| = |B| =...
Total Unique Visitors
Loading......