Use the following definitions and the laws of logic to prove the following statement. • Definition of Cartesian product: (x, y) E Ax B + (x€ A) ^ (y E B) • Definition of union: x E AUB → (x E A) V (x € B) Statement. For any sets A, B, C, A × (BUC) = (A × B) U (A × C).

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Use the following definitions and the laws of logic to prove the following statement.
• Definition of Cartesian product: (x, y) E Ax B
+ (x€ A) ^ (y E B)
• Definition of union: x E AUB → (x E A) V (x € B)
Statement. For any sets A, B, C, A × (BUC) = (A × B) U (A × C).
Transcribed Image Text:Use the following definitions and the laws of logic to prove the following statement. • Definition of Cartesian product: (x, y) E Ax B + (x€ A) ^ (y E B) • Definition of union: x E AUB → (x E A) V (x € B) Statement. For any sets A, B, C, A × (BUC) = (A × B) U (A × C).
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