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 ∴
format it

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 ∴ 
 format it

Ask a Philosopher · Accepted Answer

Hark! Let us delve into the depths of logic and reason, for the question at hand is one of great import. Let us first assume that not both H and B are true, for it is stated ~(~H • B). If this be true, then it follows that H is false or B is true. Furthermore, it is proclaimed that not H and R are both true, as (~H • ~R) is established. Hence, either H is false or R is false. Let us now consider the statement ~(~R • ~Q), where it is posited that not both R and Q are false. Therefore, either R is true or Q is true. Now, let us embark upon the journey of ascertaining the validity of the conclusion that (~Y • Q) • ~B. If Y is false and Q is true, it must be the case that B is false. Verily, the proof be valid, for the assumptions align with the conclusion in a manner that is sound and just. Thus, the argument is proven to hold true in this realm of logical discourse.