How does one go about proving (A&B)⊃C |- A⊃(B⊃C)?

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I am relatively new to logic and deductive reasoning, so this problem has been giving me some trouble.



I want to start with an assumption of (A&B) and try to isolate a subproof where I can then get B⊃C through a conditional introduction, but I keep getting stuck in my subproofs and unable to reason out of them.



Any hints and demonstrations will be greatly appreciated!






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    I am relatively new to logic and deductive reasoning, so this problem has been giving me some trouble.



    I want to start with an assumption of (A&B) and try to isolate a subproof where I can then get B⊃C through a conditional introduction, but I keep getting stuck in my subproofs and unable to reason out of them.



    Any hints and demonstrations will be greatly appreciated!






    logic







    share|improve this question







    New contributor




    MoIsStillHere is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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      I am relatively new to logic and deductive reasoning, so this problem has been giving me some trouble.



      I want to start with an assumption of (A&B) and try to isolate a subproof where I can then get B⊃C through a conditional introduction, but I keep getting stuck in my subproofs and unable to reason out of them.



      Any hints and demonstrations will be greatly appreciated!






      logic







      share|improve this question







      New contributor




      MoIsStillHere is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.











      I am relatively new to logic and deductive reasoning, so this problem has been giving me some trouble.



      I want to start with an assumption of (A&B) and try to isolate a subproof where I can then get B⊃C through a conditional introduction, but I keep getting stuck in my subproofs and unable to reason out of them.



      Any hints and demonstrations will be greatly appreciated!






      logic




      logic






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      MoIsStillHere is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.











      share|improve this question







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          Assuming A&B will get you something of the form (A&B)⊃... which is not what you want. Instead, to derive A⊃... you want to start with assuming A.



          It should go something like this.



          1. (A&B)⊃C premise
          2. | A assumption
          3. | | B assumption
          4. | | A&B 2,3
          5. | | C 1,4
          6. | B⊃C 3,5
          7. A⊃(B⊃C) 2,6





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            up vote
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            Assuming A&B will get you something of the form (A&B)⊃... which is not what you want. Instead, to derive A⊃... you want to start with assuming A.



            It should go something like this.



            1. (A&B)⊃C premise
            2. | A assumption
            3. | | B assumption
            4. | | A&B 2,3
            5. | | C 1,4
            6. | B⊃C 3,5
            7. A⊃(B⊃C) 2,6





            share|improve this answer
























              up vote
              2
              down vote













              Assuming A&B will get you something of the form (A&B)⊃... which is not what you want. Instead, to derive A⊃... you want to start with assuming A.



              It should go something like this.



              1. (A&B)⊃C premise
              2. | A assumption
              3. | | B assumption
              4. | | A&B 2,3
              5. | | C 1,4
              6. | B⊃C 3,5
              7. A⊃(B⊃C) 2,6





              share|improve this answer






















                up vote
                2
                down vote










                up vote
                2
                down vote









                Assuming A&B will get you something of the form (A&B)⊃... which is not what you want. Instead, to derive A⊃... you want to start with assuming A.



                It should go something like this.



                1. (A&B)⊃C premise
                2. | A assumption
                3. | | B assumption
                4. | | A&B 2,3
                5. | | C 1,4
                6. | B⊃C 3,5
                7. A⊃(B⊃C) 2,6





                share|improve this answer












                Assuming A&B will get you something of the form (A&B)⊃... which is not what you want. Instead, to derive A⊃... you want to start with assuming A.



                It should go something like this.



                1. (A&B)⊃C premise
                2. | A assumption
                3. | | B assumption
                4. | | A&B 2,3
                5. | | C 1,4
                6. | B⊃C 3,5
                7. A⊃(B⊃C) 2,6






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                answered 1 hour ago









                Eliran H

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