SOLUTION: I am trying to solve this proof: premises: A or B, A or C goal: A or (B and C) I know that I need to use subproofs to solve this, but I don't know how far I need to break d

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Question 1026781: I am trying to solve this proof:
premises: A or B, A or C
goal: A or (B and C)
I know that I need to use subproofs to solve this, but I don't know how far I need to break down each premise with a subproof to solve this.

Found 2 solutions by richard1234, robertb:
Answer by richard1234(7193) (Show Source):
You can put this solution on YOUR website!
Do casework based on whether A is true or not.

Case 1: A is true. Then the premise is already satisfied, and so is the goal.

Case 2: A is false. Since (A or B) is true, and (A or C) is true, it follows for the premise to hold, B must be true, and C must be true. Then (B and C) follows.

Answer by robertb(5830) (Show Source):
You can put this solution on YOUR website!
The statement is true by mathematical logic.
The premise is symbolized by (A∨B)∧(A∨C), and by the distributive property is equivalent to A∨(B∧C).
No need for long proofs or subproofs.