Exercise 3. Consider three sets X, i = 1, 2, 3, and two functions : X...
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Exercise 3. Consider three sets X₁, i = 1, 2, 3, and two functions ₁: X₁ X2 and 2: X2 → X3. Verify the following statements or find counterexamples: (1) If 1 and 2 are both injective, then 20₁ is injective. (2) If ₁ and 2 are both surjective, then 20₁ is surjective. (3) If 1 and 2 are both bijective, then 2o 1 is bijective. (4) If 1 is injective and 2 is surjective, then 201 is bijective. (5) If 201 surjective, then ₁ is surjective. (6) If 2 is injective, then 20 1 is injective. (7) If 2 is not injective, then 201 is not injective. Exercise 3. Consider three sets X₁, i = 1, 2, 3, and two functions ₁: X₁ X2 and 2: X2 → X3. Verify the following statements or find counterexamples: (1) If 1 and 2 are both injective, then 20₁ is injective. (2) If ₁ and 2 are both surjective, then 20₁ is surjective. (3) If 1 and 2 are both bijective, then 2o 1 is bijective. (4) If 1 is injective and 2 is surjective, then 201 is bijective. (5) If 201 surjective, then ₁ is surjective. (6) If 2 is injective, then 20 1 is injective. (7) If 2 is not injective, then 201 is not injective.
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Here are the counterexamples or verifications for each statement 1 True If 1 and 2 are both injectiv... View the full answer
Related Book For
Introduction to Operations Research
ISBN: 978-1259162985
10th edition
Authors: Frederick S. Hillier, Gerald J. Lieberman
Posted Date:
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