The Shino Society has exactly 3 members: Arjun, Karn, and Bhim. During one…

Concept: This is a constraint-satisfaction logic puzzle -- each member must be assigned a For/Against vote on each bill so that every bill's total-supporter count and every member's own for/against requirement hold together. Solve it by finding the one clue that pins a value directly, then propagate that fact through the remaining count constraints until the whole grid is fixed.

Application:

1. Karn already votes against the recreation bill (given). His own rule is that he votes for exactly two of the three bills; since recreation is his only confirmed 'against' so far, both of the remaining bills -- school and tax -- must be his 'for' votes.

2. Exactly one member supports the school bill (given). Karn is now a confirmed supporter of it, so he must be that lone supporter -- Arjun (given against school) and Bhim cannot also support it.

3. Exactly one member supports the tax bill (given). Karn is a confirmed supporter of it too, so he is that lone supporter -- Bhim (given against tax) cannot also support it, and Arjun must therefore be against the tax bill.

4. Exactly two members support the recreation bill (given). Arjun already supports it and Karn opposes it, so the second supporter must be Bhim.

Cross-check:

Confirm every member has at least one for-vote and one against-vote, and every bill's headcount matches:

The recreation bill totals 2 supporters (Arjun, Bhim); the school and tax bills each total exactly 1 supporter (Karn) -- every given constraint is satisfied, and each member has both a for-vote and an against-vote.

Karn votes for the school bill is therefore the true statement.