2.3 Constructing Truth Tables

For each logical statement, determine the truth value of its negation.

1. $p$: $3 + 5 = 8.$
2. $q$: All horses are mustangs.
3. $\sim r$: New Delhi is not the capital of India.

Given $p : \textrm{ } 4 + 7 = 11 ,$ $q : \textrm{ } 11 - 3 = 7 ,$ and $r : \textrm{ } 7 \times 11 = 77 ,$ determine the truth value of each conjunction.

1. $p \land q$
2. $\sim q \land r$
3. $\sim p \land q$

Given $p : \textrm{ } 4 + 7 = 11 ,$ $q : \textrm{ } 11 - 3 = 7 ,$ and $r : \textrm{ } 7 \times 11 = 77 ,$ determine the truth value of each disjunction.

1. $p \lor q$
2. $\sim q \lor r$
3. $\sim p \lor q$

Given $p : 4 + 7 = 11 ,$ $q : 11 - 3 = 7 ,$ and $r : 7 \times 11 = 77 ,$ construct a truth table to determine the truth value of each compound statement

1. $\sim p \land q \lor r$
2. $\sim p \lor q \land r$
3. $\sim \left(p \land r\right) \lor q$

Construct a truth table to analyze all possible outcomes for each of the following arguments.

1. $p \lor \sim q$
2. $\sim \left(p \land q\right)$
3. $\left(p \lor \sim q\right) \land r$

Construct a truth table to determine the validity of each of the following statements.

1. $\sim p \land q$
2. $\sim \left(p \land \sim p\right)$