Income may be recognized from cancellation of debt in which instance?

My group and I disagree on the following ones:

Income may be recognized from cancellation of debt in which instance?

The debt cancelled was intended as a gift
the debt was cancelled by a purchase price reduction
The debt would have been deductible by the taxpayer if paid
Debt cancelled was from the mortgage on a taxpayer’s second home

Boot is
Not a factor in determining basis of property received in an exchange
Cash paid or received in an exchange
Unlike property received in an exchange
Unlike property paid in an exchange

Which taxpayer is not able to deduct NOLs incurred by its entity?

A shareholder in a C corporation
A partner in a partnership
A partner in an LLC
A sole proprietor

One of the following is not a benefit of Rev Rul 2009-9.

The loss may be reported for the year of discovery or on previous year return
The loss is an ordinary theft loss, not a capital loss
The loss is reported on Form 4684
The loss is considered an investment loss not subject to the per-event floor or the 10%-of-AGI threshold.

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