statements. (a) For all sets A, B and C, if A ⊆ B ∪ C then A ⊆ B or A ⊆ C. (b) For all sets A, B and C, if A ⊆ (B − C) then A ∩ (C − B) = ∅. (c) For all sets A, B and C,if A 6 = ∅ and A × B ⊆ A × C then B ⊆ C.

statements. (a) For all sets A, B and C, if A ⊆ B ∪ C then A ⊆ B or A ⊆ C. (b) For all sets A, B and C, if A ⊆ (B − C) then A ∩ (C − B) = ∅. (c) For all sets A, B and C,if A 6 = ∅ and A × B ⊆ A × C then B ⊆ 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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3. Prove or disprove each of the following statements.
(a) For all sets A, B and C, if A ⊆ B ∪ C then A ⊆ B or A ⊆ C.
(b) For all sets A, B and C, if A ⊆ (B − C) then A ∩ (C − B) = ∅.
(c) For all sets A, B and C,if A 6 = ∅ and A × B ⊆ A × C then B ⊆ C.

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