A, B and C be sets. (a) Suppose that A ? B and B ? C....
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A, B and C be sets.
(a) Suppose that A ? B and B ? C. Does this mean that A ? C?Prove your answer. Hint: to prove that A ? C you must prove theimplication, “for all x, if x ? A then x ? C.”
(b) Suppose that A ? B and B ? C. Does this mean that A ? C?Give an example to prove that this does NOT always happen (andexplain why your example works). You should be able to give anexample where |A| = |B| = |C| = 2.
A, B and C be sets.
(a) Suppose that A ? B and B ? C. Does this mean that A ? C?Prove your answer. Hint: to prove that A ? C you must prove theimplication, “for all x, if x ? A then x ? C.”
(b) Suppose that A ? B and B ? C. Does this mean that A ? C?Give an example to prove that this does NOT always happen (andexplain why your example works). You should be able to give anexample where |A| = |B| = |C| = 2.
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