Sheridan's campaign in the Shenandoah Valley and Sherman's march through Georgia were example of General Grant's belief in A:A. merciful war.B:B. trench war.C:C. modern war.

Sure, let's break down the question step by step:

1. Identify the campaigns mentioned:

   • Sheridan's campaign in the Shenandoah Valley
   • Sherman's march through Georgia

2. Understand the context:

   • Both campaigns were part of the American Civil War.
   • General Ulysses S. Grant was a leading Union general during this war.

3. Analyze the options given:

   • A: merciful war
   • B: trench war
   • C: modern war

4. Evaluate each option in the context of the campaigns:

   • Merciful war: This option suggests a war conducted with leniency and minimal destruction. However, both Sheridan's and Sherman's campaigns were known for their harsh tactics and significant destruction, aimed at crippling the Confederate war effort.
   • Trench war: This option refers to a type of warfare characterized by the use of trenches, which was more prominent in World War I. The Civil War did see some trench warfare, but it was not the defining characteristic of these campaigns.
   • Modern war: This option implies the use of strategies and tactics that are more aligned with total war, involving significant destruction of resources and infrastructure to weaken the enemy's ability to fight. Both Sheridan's and Sherman's campaigns are examples of this approach.

5. Conclusion:

   • The correct answer is C: modern war.