Chapter 3, Problem 1T

Use the following representations in Exercises 1-6:

p: I’m registered.

q: I’m a citizen.

r: I vote.

Express each compound statement in English.

$(p\wedge q)\to r$

To determine

The provided compound statement in English $\left(p\wedge q\right)\to r$.

Representations are as follows:

p: I’m registered.

q: I’m a citizen.

r: I vote.

Answer to Problem 1T

Solution:

The statement: “If I’m registered and I’m a citizen, then I vote.”

Explanation of Solution

Given:

The compound statement: $\left(p\wedge q\right)\to r$.

Representations are as follows:

p: I’m registered.

q: I’m a citizen.

r: I vote.

Explanation:

Conjunction statement is

$p\wedge q$: p and q.

Conditional statement is

$\left(p\wedge q\right)\to r$: If p and q, then r.

Use the representations to write the compound statement in English as

“If I’m registered and I’m a citizen, then I vote.”