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Unformatted text preview: ′ , c ′ , b ′ d ′ ). ( a, b ) ∼ ( a ′ , b ′ ) ⇐⇒ ab ′ = a ′ b, (1) ( c, d ) ∼ ( c ′ , d ′ ) ⇐⇒ cd ′ = c ′ d. (2) Multiplying the frst by cd ′ and substituting in the second gives ab ′ cd ′ = a ′ bcd ′ = a ′ bc ′ d. Q. E. D. Problem 3: (2 points) Label the Following true or False (a) (0.5 points) T Q is an ordered feld. (b) (0.5 points) ± A feld need not be an integral domain. (c) (0.5 points) ± Let X be a nonempty set and ℘ ( X ) be the power set oF X . Then ℘ ( X ) with △ as ‘+’ and ∩ as ‘ · ’ is a feld. (d) (0.5 points) ± A subset oF A × B such that each element oF A occurs exactly once as a frst coordinate is called an injective Function. 2...
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 Fall '07
 SCHMIDT
 Inverse function, Finite set, Basic concepts in set theory

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