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True or False? 1. Let f : R → R be a function defined by f(x) = x^2+1. If B = {2, 5}, then f^(−1)[B] = {1, 2}.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

True or False?

1. Let f : R → R be a function defined by f(x) = x^2+1. If B = {2, 5}, then f^(−1)[B] = {1, 2}.
2. Let R be an equivalence relation on A = {w, x, y, z}. If wRx, yRz, and wRz, then xRy.
3. For every nonempty set A, there exists a relation R which is both an equivalence relation
and a partial ordering on A.

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Similar questions

2. Recall that if R is a relation, then we can look at the inverse relation R^ -1 ={ (y,x):(x,y) in R} . Show that for a function F: X -> Y, F ^ - 1 is a (total) function if and only if F is bijective.
Let R be the relation on R defined by Ry if and only if ry 1. Thus R can also be represented as (r, y) ry = 1} . Use a similar representation for each of your answers to the questions below, and write your answer in the accompanying box What is the composite relation R2 ? (a) (b) What is the composite relation R3? What is the composite relation R4? (c) (d) What is the transitive closure of R?
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Determine whether the given relation is an equivalent relation on (1, 2, 3, 4, 5} If the relation is an equivalence relation, list the equivalence classes (x, y E {1,2, 3, 4, 5} . ) 3, 4, 5}. 1. {(1,1), (2, 2) , (3, 3) , (4, 4) , (5, 5) , (1, 3) , (3, 1)} 2. {(x, y) | 3 divides x + y}
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Please help me answer how is number 1 (For every element x in A, there is an element y in B such that (x,y) is in F ) differ from a relation? Please explain this!