Premise — Definition, Formula & Examples
A premise is a statement assumed or known to be true that serves as the starting point for a logical argument or proof. The conclusion of the argument follows from one or more premises.
In deductive reasoning, a premise is a proposition from which a conclusion is logically derived. In a valid argument, if all premises are true, the conclusion must necessarily be true.
How It Works
When you construct a proof or logical argument, you begin with premises — these are the "given" information. You then apply logical rules to move from the premises to a conclusion. In a conditional statement like "if , then ," the premise is (the hypothesis) and the conclusion is . An argument can have multiple premises that work together. For example, in a two-column geometry proof, the premises are listed as your "given" statements at the top.
Example
Problem: Identify the premises and conclusion in this argument: All squares are rectangles. ABCD is a square. Therefore, ABCD is a rectangle.
Identify Premise 1: The first statement assumed to be true is:
Identify Premise 2: The second given statement is:
Identify the Conclusion: The statement that follows logically from both premises is:
Answer: Premise 1: All squares are rectangles. Premise 2: ABCD is a square. Conclusion: ABCD is a rectangle. The conclusion is valid because it follows necessarily from the two premises.
Why It Matters
Recognizing premises is essential in geometry proofs, where every deduction must trace back to given information or previously proven statements. Beyond math class, identifying premises helps you evaluate whether everyday arguments are logically sound — a core skill in computer science, law, and philosophy.
Common Mistakes
Mistake: Confusing the premise with the conclusion in a conditional statement.
Correction: In "if , then ," the premise (hypothesis) is and the conclusion is . The word after "if" is the premise; the word after "then" is the conclusion.