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>In Strategy

Learn step-by-step guide on structuring your proof from bottom up for effective problem-solving. Avoid common mistakes for a successful outcome in mathematical proofs.

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>In Strategy

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  1. >In Strategy When working with >In, it is important to develop The structure of your proof from bottom up. 1 1.A>(S>C) A [1] 1 (A&S)>C GOAL [2]

  2. >In Strategy When working with >In, it is important to develop The structure of your proof from bottom up. 1 1.A>(S>C) A [1] 2 2. A&S PA [3] C GOAL [4] 1 (A&S)>C 2-?>I [2]

  3. >In Strategy When working with >In, it is important to develop The structure of your proof from bottom up. 1 1.A>(S>C) A [1] 2 2. A&S PA [3] 2 3. A 2&O [5] 2 4. S 2&O [6] C GOAL [4] 1 (A&S)>C 2-?>I [2]

  4. >In Strategy When working with >In, it is important to develop The structure of your proof from bottom up. 1 1.A>(S>C) A [1] 2 2. A&S PA [3] 2 3. A 2&O [5] 2 4. S 2&O [6] 1,2 5. S>C 1,3>O [7] C GOAL [4] 1 (A&S)>C 2-?>I [2]

  5. >In Strategy When working with >In, it is important to develop The structure of your proof from bottom up. 1 1.A>(S>C) A [1] 2 2. A&S PA [3] 2 3. A 2&O [5] 2 4. S 2&O [6] 1,2 5. S>C 1,3>O [7] 1,2 6. C 5,4>O [4] 1 7. (A&S)>C 2-6>I [2]

  6. >In Strategy When working with >In, it is important to develop The structure of your proof from bottom up. 1 1.A>(S>C) A [1] 2 2. A&S PA [3] 2 3. A 2&O [5] 2 4. S 2&O [6] 1,2 5. S>C 1,3>O [7] 1,2 6. C 5,4>O [4] 1 7. (A&S)>C 2-6>I [2]

  7. >In Strategy WHAT NOT TO DO! (USE PA FROM THE TOP) 1 1.A>(S>C) A 2 2. A PA BAD! 1,2 3. S>C 1,2>O ????? 1 (A&S)>C GOAL

  8. >In Strategy WHAT NOT TO DO! (USE PA FROM THE TOP) 1 1.A>(S>C) A 2 2. A PA 1,2 3. S>C 1,2>O 4 4. S PA BAD! 1,2,4 5. C 3,4>O ????? 1 (A&S)>C GOAL

  9. >In Strategy WHAT NOT TO DO! (USE PA FROM THE TOP) 1 1.A>(S>C) A 2 2. A PA 1,2 3. S>C 1,2>O 4 4. S PA 1,2,4 5. C 3,4>O 1,2 6. S>C 4-5>I ????? 1 (A&S)>C GOAL

  10. >In Strategy WHAT NOT TO DO! (USE PA FROM THE TOP) 1 1.A>(S>C) A 2 2. A PA 1,2 3. S>C 1,2>O 4 4. S PA 1,2,4 5. C 3,4>O 1,2 6. S>C 4-5>I 1 7. A>(S>C) 2-6>I ????? 1 (A&S)>C GOAL

  11. >In Strategy 1 1.(A&S)>C A [1] 1 A>(S>C) GOAL [2]

  12. >In Strategy 1 1.(A&S)>C A [1] 2 2. A PA [3] S>C GOAL [4] 1 A>(S>C) 2-? >I [2]

  13. >In Strategy 1 1.(A&S)>C A [1] 2 2. A PA [3] 3 3. S PA [5] C GOAL [6] S>C 3-? >I [4] 1 A>(S>C) 2-? >I [2]

  14. >In Strategy 1 1.(A&S)>C A [1] 2 2. A PA [3] 3 3. S PA [5] C GOAL [6] S>C 3-? >I [4] 1 A>(S>C) 2-? >I [2]

  15. >In Strategy 1 1.(A&S)>C A [1] 2 2. A PA [3] 3 3. S PA [5] A&S GOAL [7] C 1,? >O [6] S>C 3-? >I [4] 1 A>(S>C) 2-? >I [2]

  16. >In Strategy 1 1. (A&S)>C A [1] 2 2. A PA [3] 3 3. S PA [5] 2,3 4. A&S 2,3 &I [7] 1,2,3 5. C 4,1 >O [6] 1,2 6. S>C 3-5 >I [4] 1 7. A>(S>C) 2-6 >I [2] MORAL: KEEP YOUR EYES DOWN. USE THE BOTTOM OF THE PROOF TO FIGURE OUT THE CORRECT PA.

  17. >In and &In Together 1 1. T>(L&M) A [1] 1 (T>L)&(T>M) GOAL [2] When you have A&B as a GOAL Try to prove A and B separately. Then paste them together with &In.

  18. >In and &In Together 1 1. T>(L&M) A [1] T>L GOAL [4] T>M GOAL [3] 1 (T>L)&(T>M) ?,? &I [2] When you have A&B as a GOAL Try to prove A and B separately. Then paste them together with &In.

  19. >In and &In Together 1 1. T>(L&M) A [1] T>L GOAL [4] T PA [5] M GOAL [6] T>M ?-? >I [3] 1 (T>L)&(T>M) ?,? &I [2] To prove T>M, set up a subproof with T as PA and M as your new GOAL. When the subproof is completed, use >In to obtain T>M

  20. >In and &In Together 1 1. T>(L&M) A [1] T>L GOAL [4] T PA [5] L&M 1,? >O [7] M ? &O [6] T>M ?-? >I [3] 1 (T>L)&(T>M) ?,? &I [2]

  21. >In and &In Together 1 1. T>(L&M) A [1] T>L GOAL [4] T PA [5] L&M 1,? >O [7] M ? &O [6] T>M ?-? >I [3] 1 (T>L)&(T>M) ?,? &I [2]

  22. >In and &In Together 1 1. T>(L&M) A [1] 2 2. T PA [8] L GOAL [9] T>L 2-?>I [4] T PA [5] L&M 1,? >O [7] M ? &O [6] T>M ?-? >I [3] 1 (T>L)&(T>M) ?,? &I [2] To prove T>L, set up a subproof with T as PA and L as your new GOAL. When the subproof is completed, use >In to obtain T>L.

  23. >In and &In Together 1 1. T>(L&M) A [1] 2 2. T PA [8] 1,2 3. L&M 1,2 >O [10] 1,2 4. L 3 &O [9] 1 5. T>L 2-4>I [4] 6 6. T PA [5] 1,6 7. L&M 1,6 >O [7] 1,6 8. M 7 &O [6] 1 9. T>M 6-8 >I [3] 1 10. (T>L)&(T>M) 5,9 &I [2] For more click here

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