Explanatory Question
Prove that \( X + 1 \) is a tautology.
Read the answer carefully and go through the related questions on the right side to improve your understanding of this topic.
Prove that \( X + 1 \) is a tautology.
A tautology is defined as a proposition having nothing but 1's in its truth table column. To prove this for the given expression, a truth table is constructed to evaluate \( X + 1 \) for all possible values of \( X \).
Truth Table for \( X + 1 \):
| \( X \) | \( 1 \) | \( X + 1 \) |
|---|---|---|
| 0 | 1 | 1 |
| 1 | 1 | 1 |
Conclusion:
Since the column for \( X + 1 \) contains only trues (1's), the expression is confirmed to be a tautology.
First read the answer fully, then try to explain it in your own words. After that, open a few related questions and compare the concepts. This method helps you remember the topic for a longer time and improves exam preparation.