Question: Exercise 3. Consider three sets X, i = 1, 2, 3, and two functions : X X2 and 2: X2 X3. Verify the following

Exercise 3. Consider three sets X, i = 1, 2, 3, and two functions : X X2 and 2: X2 X3. Verify the following

(7) If 2 is not injective, then 201 is not injective.

Exercise 3. Consider three sets X, i = 1, 2, 3, and two functions : X X2 and 2: X2 X3. Verify the following statements or find counterexamples: (1) If 1 and 2 are both injective, then 20 is injective. (2) If and 2 are both surjective, then 20 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 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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