2) The two statements are not equivalent 3) By transitivity, since A < B and B < C, it follows that A < C
Logical Equivalences:
For Statement 1:

Applying De Morgan's Law:

Applying De Morgan's Law again:

By distributing:

Simplify:

For Statement 2:

The two statements are not equivalent.
3) Direct Proof:
For the statement "If A < B, and B < C, then A < C":
Assume A < B and B < C are both true.
By transitivity, since A < B and B < C, it follows that A < C
Thus, the statement is proven using the direct method.
Complete Question:
(2) Use logical equivalences to perform a direct proof that the two following logical statements are equivalent. (20 pts.) Statement 1: !(P OR (IP AND Q)) Statement 2: IP AND IQ (3) Prove the following statement using the Direct Method. (20 pts.) If A<B, and B <C, then AC (4) Convert the following from the base