Question

Example 1 Identify the hypothesis and conclusion of each statement.

If $\mathit{x}$equals$\mathit{y}$and$\mathit{y}$equals$\mathit{z}$, then$\mathit{x}$equals$\mathit{z}$.

Short answer

The hypothesis is “ equals $x$and $y$equals $z$” and the conclusion of the given statement is “$x$ equals $z$”.

Step-by-step solution

Step 1. State the concept.

In an if-then statement, the part of the statement immediately following “if” is the hypothesis, and the part of the statement immediately following “then” is the conclusion.

Step 2. List the given data.

The given statement is “If $x$equals $y$and $y$equals $z$, then$x$ equals $z$.”

Step 3. Find the hypothesis.

The part of the given statement immediately following “if” is “$x$ equals $y$and $y$equals $z$”. Then, the hypothesis is “$x$ equals $y$and $y$equals $z$”.

Step 4. Find the conclusion.

The part of the given statement immediately following “then” is “$x$ equals $z$”. Then, the conclusion is “$x$ equals $z$”.