For this question you should use reasoning patterns which are either explicitly listed in the subject guide, pp.20-22, or can be produced using the logical equivalences in Figure 4.1 of the guide. Explain whether the 'proofs' in i-iii below are correct according to the reasoning patterns and equivalences given in the guide. If not, give a correct proof showing what can be inferred from the knowledge base provided. Show all steps in your reasoning and explain your answers. i. Knowledge base: 1. AAB 2. B ( CD) 3. A--D Proof: A ABIA A AB/B B- ( CD).B/ CD A, A+ -D/-D -D C-D/-C ii Knowledge base: 1. (AB) 2. AVB 3. BC 4. C Proof: (A ABY-AAB A AB-A AVB A/B B-C. B/C iii. Knowledge base: 1. (A v B) 2. AC 3. CD 4. DB Proof: -(A v B)/-AAB AAB-A -A, A-C/-c -C, CD/-D For this question you should use reasoning patterns which are either explicitly listed in the subject guide, pp.20-22, or can be produced using the logical equivalences in Figure 4.1 of the guide. Explain whether the 'proofs' in i-iii below are correct according to the reasoning patterns and equivalences given in the guide. If not, give a correct proof showing what can be inferred from the knowledge base provided. Show all steps in your reasoning and explain your answers. i. Knowledge base: 1. AAB 2. B ( CD) 3. A--D Proof: A ABIA A AB/B B- ( CD).B/ CD A, A+ -D/-D -D C-D/-C ii Knowledge base: 1. (AB) 2. AVB 3. BC 4. C Proof: (A ABY-AAB A AB-A AVB A/B B-C. B/C iii. Knowledge base: 1. (A v B) 2. AC 3. CD 4. DB Proof: -(A v B)/-AAB AAB-A -A, A-C/-c -C, CD/-D