Let X = {a,b,c} prove that topological space on the set X T = {X. Ø, {b}, {a,b}} be a
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- Give an example of mappings and such that one of or is not onto but is onto.Find mappings f,g and h of a set A into itself such that fg=hg and fh. Find mappings f,g and h of a set A into itself such that fg=fh and gh.Label each of the following statements as either true or false. 3. Let , , and be mappings from into such that . Then .
- Suppose thatis an onto mapping from to. Prove that if ℒ, is a partition of, then ℒ, is a partition of.Label each of the following statements as either true or false. Every mapping on a nonempty set A is a relation.10. Let and be mappings from to. Prove that if is invertible, then is onto and is one-to-one.
- Label each of the following statements as either true or false. Let f:AB. Then f(A)=B for all nonempty sets A and B.Label each of the following statements as either true or false. The least upper bound of a nonempty set S is unique.Label each of the following statements as either true or false. A mapping is onto if and only if its codomain and range are equal.