Nope, it's a Constitutional Representative Republic. The US is not a pure democracy due to the electoral college system we have.

We are constitutionally a republic.

We are both a democracy and a Republic. Therefore, we are a Democratic Republic.

Nice syllogism attempt. Our constitution is fully a republic. Therefore, our government is a republic. When Franklin left the constitutional convention, a woman asked him, "well, do we have a monarchy or a republic?" Franklin famously responded by saying, "a republic, Madame. If you can keep it."

No syllogism here; considering nothing was assumed. Our government is controlled by the people but we also elect officials. Democratic Republic.

Recite the pledge of allegiance.

Ah yes, the "oath" that was heavily altered during the Cold War. If you're referring to the line that states "to the Republic...", that isn't relevant. I don't know why it's so hard for you to understand what a Democratic Republic is. The US is a Democratic Republic. The government is run by the people; democracy. The people elect officials; republic. Therefore, a Democratic Republic. What is so difficult to comprehend.

The United States is, indeed, a republic, not a democracy. Accurately defined, a democracy is a form of government in which the people decide policy matters directly--through town hall meetings or by voting on ballot initiatives and referendums. A republic, on the other hand, is a system in which the people choose representatives who, in turn, make policy decisions on their behalf. The Framers of the Constitution were altogether fearful of pure democracy. Everything they read and studied taught them that pure democracies "have ever been spectacles of turbulence and contention; have ever been found incompatible with personal security or the rights of property; and have in general been as short in their lives as they have been violent in their deaths"