Computer Science
Show that the given statements are tautologies:
[(p ⇒ q) ^ (q ⇒ r)] ⇒ (p ⇒ r)
Boolean Algebra
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Answer
| p | q | r | p⇒q | q⇒r | (p⇒q) ^(q⇒r) | (p⇒r) | [(p⇒q) ^(q⇒r)] ⇒(p⇒r) |
|---|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 |
| 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 |
| 0 | 1 | 0 | 1 | 0 | 0 | 1 | 1 |
| 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 |
| 1 | 0 | 1 | 0 | 1 | 0 | 1 | 1 |
| 1 | 1 | 0 | 1 | 0 | 0 | 0 | 1 |
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
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