Logic Gates

Step 1: Logical equivalence. The logical statement is equivalent to its own form. There is no change in the equivalence.
Step 2: Conclusion. Thus, the equivalent statement is .

Step 1: Recall when implication is false.

So we must have:

and

Step 2: Make false.
OR statement is false only if both parts are false:

Step 3: .
So:

Final Answer:

Step 1: Analyze the logical operation.
For the logical OR operation , it is false when both and are false.
Step 2: Conclusion.
Thus, is false when both and are false.
Final Answer:

Step 1: Evaluating the logical expression.
Since and , is T. Therefore, is F.

Step 2: Conclusion.
The truth value is F, corresponding to option (2).

Step 1: Logical expression equivalency.
Using logical equivalencies, is equivalent to .

Step 2: Conclusion.
The correct equivalence is , corresponding to option (2).

By applying De Morgan’s Law and simplifying the expression, we find that the negation of the given logical expression is .

The logical implication is equivalent to , which can be verified by truth tables.

The given logical expression evaluates to true based on the truth table for the logical operators used in the expression.

Use basic matrix operations to calculate the determinant and solve for the matrix.

Step 1: Analyze the Truth Table.
From the truth table, it is evident that is true when is true and is false. Therefore, the expression for is .
Step 2: Conclusion.
The correct answer is (C), .

Step 1: Understand the negation.
The negation of a conditional statement is .
Step 2: Conclusion.
Thus, the negation of the proposition is .
Final Answer:

The conditional is always true for all values of and , making it a tautology.
Final Answer:

Step 1: In the statement , the correct connective is "or," as one of the conditions is true.

Final Answer:

Using logical equivalences, the inverse of the statement is .
Final Answer: