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Hypothesis — Definition, Meaning & Examples

Hypothesis

The part of a conditional after If and before then. In the conditional "If a line is horizontal, then the line has slope 0" the hypothesis is "a line is horizontal".

 

 

 

See also

Conclusion, converse, contrapositive, inverse of a conditional

Example

Problem: Identify the hypothesis and conclusion in the conditional statement: "If a triangle has three equal sides, then it is equilateral."
Step 1: Locate the if-then structure. The statement follows the form "If P, then Q."
Step 2: Identify the hypothesis (P). The hypothesis is the clause that comes after "if" and before "then." Here that is: "a triangle has three equal sides."
Step 3: Identify the conclusion (Q). The conclusion is the clause that comes after "then." Here that is: "it is equilateral."
Step 4: In symbolic form, let P = "a triangle has three equal sides" and Q = "it is equilateral." The conditional is written as:
P→QP \rightarrow Q
Answer: The hypothesis is "a triangle has three equal sides." The conclusion is "it is equilateral."

Another Example

Problem: Rewrite the statement "All right angles measure 90°" as a conditional, and identify the hypothesis.
Step 1: Not every statement is written in if-then form. Rewrite it: "If an angle is a right angle, then it measures 90°."
Step 2: The hypothesis is the part after "if" and before "then": "an angle is a right angle."
Step 3: The conclusion is: "it measures 90°."
Answer: The hypothesis is "an angle is a right angle."

Frequently Asked Questions

What is the difference between the hypothesis and the conclusion in a conditional statement?
The hypothesis is the condition — the "if" part. The conclusion is the result — the "then" part. In "If P, then Q," P is the hypothesis and Q is the conclusion. The hypothesis is what you assume to be true; the conclusion is what follows from that assumption.
How do you find the hypothesis when the statement is not written in if-then form?
Rewrite the statement as a conditional first. For example, "Parallel lines never intersect" becomes "If two lines are parallel, then they never intersect." The hypothesis is then "two lines are parallel." Look for the underlying condition that causes the result.

Hypothesis vs. Conclusion

In the conditional P→QP \rightarrow Q, the hypothesis is PP (the "if" clause) — the condition assumed to be true. The conclusion is QQ (the "then" clause) — the result that follows. Swapping them creates the converse, which is a different statement and may not have the same truth value as the original.

Why It Matters

Identifying the hypothesis correctly is essential for writing proofs in geometry and logic. When you prove a conditional statement, you start by assuming the hypothesis is true and then show the conclusion must follow. This skill also matters when forming the converse, inverse, and contrapositive of a statement, since each rearranges or negates the hypothesis and conclusion in a specific way.

Common Mistakes

Mistake: Confusing the hypothesis with the conclusion — placing the "then" part where the "if" part should be.
Correction: Always remember: the hypothesis comes after "if" and before "then." It is the condition, not the result. A helpful mnemonic: the Hypothesis is what you Have to start with.
Mistake: Assuming the converse is automatically true whenever the original conditional is true.
Correction: The converse swaps the hypothesis and conclusion. "If Q, then P" can be false even when "If P, then Q" is true. For example, "If a shape is a square, then it is a rectangle" is true, but the converse "If a shape is a rectangle, then it is a square" is false.

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