1. (10 points) Fix ? = {0,1} for this question. True/False Briefly justify each answer: a. Every language mapping reduces to its complement b. For languages A, B if A mapping reduces to B and B mapping reduces to A then A- B c. For languages A, B if A mapping reduces to B then B mapping reduces to A d. Every decidable language mapping reduces to 0 eD" mapping reduces to every nonempty language over ?. Recall mapping reduction is defined in section 5.3: The problem A mapping reduces to B means there is a computable function f : ?* ? ?* such that for all z E ? zEA iff f(x) E B A computable function that makes the "iff true is said to witness the mapping reduction from A to B. 1. (10 points) Fix ? = {0,1} for this question. True/False Briefly justify each answer: a. Every language mapping reduces to its complement b. For languages A, B if A mapping reduces to B and B mapping reduces to A then A- B c. For languages A, B if A mapping reduces to B then B mapping reduces to A d. Every decidable language mapping reduces to 0 eD" mapping reduces to every nonempty language over ?. Recall mapping reduction is defined in section 5.3: The problem A mapping reduces to B means there is a computable function f : ?* ? ?* such that for all z E ? zEA iff f(x) E B A computable function that makes the "iff true is said to witness the mapping reduction from A to B