Question

The following table shows the value of expression based on the values of input1 and input2.
Value of input1 Value of input2 Value of expression
true true false
true false true
false true true
false false true

Question
63

Mark for Review

Which of the following expressions are equivalent to the value of expression as shown in the table?

Select two answers.

(NOT input1) OR (NOT input2)
Option A,(NOT input1) OR (NOT input2)

(NOT input1) AND (NOT input2)
Option B,(NOT input1) AND (NOT input2)

NOT (input1 OR input2)
Option C,NOT (input1 OR input2)

NOT (input1 AND input2)

Answer 1

To determine which expressions are equivalent to the value of the expression shown in the table, we can analyze the provided truth values.

The table can be interpreted as follows:

- **When input1 is true and input2 is true**: expression is false
- **When input1 is true and input2 is false**: expression is true
- **When input1 is false and input2 is true**: expression is true
- **When input1 is false and input2 is false**: expression is true

We can summarize the results:
- expression is true when (input1, input2) is (true, false), (false, true), or (false, false)
- expression is false when (input1, input2) is (true, true)

This setup matches the following logical condition: the expression is false when both inputs are true, which can be represented as:

**NOT (input1 AND input2)**

Now, let's evaluate the given options:

1. **(NOT input1) OR (NOT input2)**:
- This expression is true unless both input1 and input2 are true, which can be interpreted as the distribution of false when both are true. Thus, this expression is equivalent to the outcome described by the table.

2. **(NOT input1) AND (NOT input2)**:
- This expression is only true when both input1 and input2 are false, which does not match all true outcomes in the table. Thus, this option is not equivalent.

3. **NOT (input1 OR input2)**:
- As per De Morgan's laws, this expression is equivalent to (NOT input1) AND (NOT input2), which is not equivalent to the table conditions. Thus, this option is also not equivalent.

4. **NOT (input1 AND input2)**:
- This expression is true unless both inputs are true, which aligns with the table when both inputs are true, so this is equivalent.

In conclusion, the two expressions from the options that are logically equivalent to the value of expression shown in the table are:

- Option A: (NOT input1) OR (NOT input2)
- Option D: NOT (input1 AND input2)

Choose:
**(NOT input1) OR (NOT input2)** and **NOT (input1 AND input2)**.