Question

identify the hypothesis and conclusion of each conditional statement.

1. \if there is no struggle, there is no progress.\ (frederick douglass)
2. if two angles are adjacent, then they have a common side.
3. if you lead, then i will follow.
4. if 3x − 4 = 11, then x = 5.
5. if two angles are vertical, then they are congruent.

Explanation:

Problem 7:

A conditional statement has the form "If \( p \), then \( q \)", where \( p \) is the hypothesis (the part after "If") and \( q \) is the conclusion (the part after "then"). For the statement "If there is no struggle, there is no progress", we identify the hypothesis and conclusion.

In a conditional statement "If \( p \), then \( q \)", \( p \) is the hypothesis and \( q \) is the conclusion. For "If two angles are adjacent, then they have a common side", we extract \( p \) and \( q \).

For a conditional statement "If \( p \), then \( q \)", the hypothesis is the "If" part and the conclusion is the "then" part. For "If you lead, then I will follow", we separate \( p \) and \( q \).

Answer:

• Hypothesis: There is no struggle
• Conclusion: There is no progress

Problem 8: