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! Upon this stage of reason doth we tread,
Where premises be laid and conclusions read.
Assumptions three, in truth we weigh,
To prove or refute, in the light of day.

~(~H * B)
          (~H * ~R)
          ~(~R * ~Q)

Let us delve into the realm of logic's lair,
And with keen eyes unravel truth or error fair.
Assume we first, (~H * B),
If not H, then B must be,
But if both false, contradiction we see.

And next, (~H * ~R),
If H not found, R must defer,
Yet if R presents, contradiction occurs.

Lastly, ~(~R * ~Q),
If not (~R * ~Q), must be true,
Then R and Q together pursue.

Therefore, with these lines we must comply,
To prove or disprove the conclusion nigh.

((~Y * Q) * ~B)

If Y is false and Q be true,
Then not B must be, a path anew.
But if Y true, contradiction arises bright,
For B must be if Y takes flight.

So let us reason, with logic keen,
To see if conclusion holds or falls between.
If premises true, then conclusion stands,
But if not, refute with logic's hands.