Question

statements, conditionals, and biconditionals · practice
examples 1 and 2
use the statements to write a compound statement for each conjunction or disjunction.
then find the truth values. explain your reasoning.
$p:-3 - 2=-5$
$q$: vertical angles are congruent.
$r:2 + 8>10$

1. $p$ and $q$ 2. $pwedge r$ 3. $qveesim r$
2. $rvee q$ 5. $sim pwedgesim q$ 6. $sim rveesim p$

example 3
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:

• For conditional statements in the form "If \(p\), then \(q\)", the hypothesis is \(p\) and the conclusion is \(q\).

Answer:

• 7. Hypothesis: There is no struggle. Conclusion: There is no progress.
• 8. Hypothesis: Two angles are adjacent. Conclusion: They have a common side.
• 9. Hypothesis: You lead. Conclusion: I will follow.
• 10. Hypothesis: \(3x - 4=11\). Conclusion: \(x = 5\).
• 11. Hypothesis: Two angles are vertical. Conclusion: They are congruent.