5. Let f : A → B with C, C1,C2 C A and D C B.(a) Show that if f is INJECTIVE (ONE-TO-ONE) thenf[f(C)] = C.(b) Show that if f is SURJECTIVE (ONTO) thenf[f-'(D)] = D.(c) Show that if f is INJECTIVE (ONE-TO-ONE) thenf(C,nC)] = f(C;)n f(C2). 2. Use truth tables to show that the statement~ (PAQ)is logically equivalent to(~ P) V (~ Q).

"Since you have posted multiple questions, we will answer the first question. If you want the…

Let f : A B with C, C1, C2 C A and DC B. (a) Show that if f is INJECTIVE (ONE-TO-ONE) then ff(C)] = C. (b) Show that if f is SURJECTIVE (ONTO) then fI(D)] = D. (c) Show that if f is INJECTIVE (ONE-TO-ONE) then f(C,nC)] = f(C1)n f(C).

Let f : A B with C, C1, C2 C A and DC B. (a) Show that if f is INJECTIVE (ONE-TO-ONE) then ff(C)] = C. (b) Show that if f is SURJECTIVE (ONTO) then fI(D)] = D. (c) Show that if f is INJECTIVE (ONE-TO-ONE) then f(C,nC)] = f(C1)n f(C).

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

5. Let f : A → B with C, C1,C2 C A and D C B.
(a) Show that if f is INJECTIVE (ONE-TO-ONE) then
f[f(C)] = C.
(b) Show that if f is SURJECTIVE (ONTO) then
f[f-'(D)] = D.
(c) Show that if f is INJECTIVE (ONE-TO-ONE) then
f(C,nC)] = f(C;)n f(C2).

2. Use truth tables to show that the statement
~ (PAQ)
is logically equivalent to
(~ P) V (~ Q).

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