Question

Question was provided via image upload.

Explanation:

Negate the conditional statement

Using the Conditional Statements knowledge point
The original statement is: "If it is night, it is dark."
Let \(p\) be "It is night" and \(q\) be "It is dark."
The statement is \(p
ightarrow q\).
The negation is \(
eg(p
ightarrow q) \equiv p \land
eg q\).
In words, this is: "It is night and it is not dark."

Construct the truth table

Using the Truth Tables knowledge point

$$
LATEXBLOCK0
$$

Since all truth values in the final column are True, the statement is a tautology.

Write converse, inverse, and contrapositive

Using the Conditional Statements knowledge point
The conditional statement is: "If you don't build it, he will come."
Let \(p\) be "You don't build it" and \(q\) be "He will come."

• Converse (\(q

ightarrow p\)): "If he will come, you don't build it."

• Inverse (\(

eg p
ightarrow
eg q\)): "If you build it, he will not come."

• Contrapositive (\(

eg q
ightarrow
eg p\)): "If he will not come, you build it."

Answer:

Question 4

"It is night and it is not dark."

Question 5

The truth table for \(q
ightarrow (p
ightarrow q)\) is:

\(p\)

\(q\)

\(p

ightarrow q\) | \(q
ightarrow (p
ightarrow q)\) |

T	T	T	T
T	F	F	T
F	T	T	T
F	F	T	T

The statement is a tautology.

Question 6

• A. Converse: "If he will come, you don't build it."
• B. Inverse: "If you build it, he will not come."
• C. Contrapositive: "If he will not come, you build it."