45 lines
1.1 KiB
Markdown
45 lines
1.1 KiB
Markdown
1. George Boole
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2. Truth Tables for a) Negation b) Contraposition
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a)
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Negation Law
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¬¬p ≡ p
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| p | ¬p | ¬(¬p) | ¬(¬p) ⇔ p |
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| --- | --- | ----- | --------- |
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| T | F | T | T |
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| F | T | F | T |
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b)
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Contraposition Law
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p ⇒ q ≡ ¬q ⇒ ¬p
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| p | ¬p | q | ¬q | p ⇒ q | ¬q ⇒ ¬p | p ⇒ q ⇔ ¬q ⇒ ¬p |
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| --- | --- | --- | --- | ----- | ------- | --------------- |
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| T | F | T | F | T | T | T |
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| T | F | F | T | F | F | T |
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| F | T | T | F | T | T | T |
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| F | T | F | T | T | T | T |
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p ⇒ q ⇔ ¬q ⇒ ¬p MUST be true, since p ⇒ q and ¬q ⇒ ¬p are shown in the truth table to be the same logical equivalence
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1. Provide names of laws
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1. Negation Law
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2. De Morgan's Law
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3. Negation Law
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4. De Morgan's Law
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5. Negation Law Twice
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6. Associative Law
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7. De Morgan's Law
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8. De Morgan's Law
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9. Negation Law Twice
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2. Show logical equivalence
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p ⇒ q
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¬q ⇒ ¬p
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p ⇒ q
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≡ (¬p) v q
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≡ q v (¬p)
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≡ ¬ (¬q) v (¬p)
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≡ (¬q) ⇒ (¬p)
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