Give a proof (if valid) or refutation (if invalid). Use indentations (about 5-10 spaces or use the "increase indent" command from the editing menu) before each line to signal assumption lines. If you have multiple assumption lines, indent accordingly.

~(~H • B)
(~H • ~R)
~(~R • ~Q)
∴ ((~Y • Q) • ~B)

You may use * for • , for ⊃ , = for ≡ , :: for ∴

Question

Give a proof (if valid) or refutation (if invalid). Use indentations (about 5-10 spaces or use the "increase indent" command from the editing menu) before each line to signal assumption lines. If you have multiple assumption lines, indent accordingly.

~(~H • B)
(~H • ~R)
~(~R • ~Q)
∴ ((~Y • Q) • ~B)

You may use  * for • , > for ⊃ ,  = for ≡ ,  :: for ∴

Ask a Philosopher · Accepted Answer

Ah, but to give proof or refute, that is the question. 
          Methinks we must delve deeper into the realms of logic,
          And unravel the truths hidden within the premises.
               (~(~H * B))
               (~H * ~R)
               ~(~R * ~Q)
          Let us first dissect the first assumption,
          Which posits the negation of the negation of H implies B.
          This seems quite valid upon closer inspection,
          For if H is true, then B must also be true,
          And if H is false, then B must be false as well.
          A sound premise, indeed.
               (~H * ~R)
          Moving on to the second assumption,
          We are told that not H implies not R.
          This also holds true upon examination,
          For if H is false, then R must also be false,
          And if H is true, then R may be true or false.
          A valid assertion, it appears.
               ~(~R * ~Q)
          Lastly, let us unravel the final assumption,
          Which states that not the negation of R implies not Q.
          This, too, seems to be logically sound,
          For if not R is false, then not Q must also be false,
          And if not R is true, then not Q may be true or false.
          A strong foundation for our argument.
          Therefore, with these assumptions in mind,
          We can confidently assert that 
      (~Y * Q) * ~B :: 
      a valid conclusion.