Exercise 1

- This is a
`FALSE`

proposition. - Predicate. It is equivalent to the predicate
`x > 0`

. - This is a
`FALSE`

proposition. - This is a
`TRUE`

proposition. - This is a
`FALSE`

proposition.

Exercise 2

If you compare the truth tables for `A ∧ B`

and `A | B`

, you’ll notice a pattern:

A |
B |
A ∧ B |
A | B |

`T` |
`T` |
`T` |
`F` |

`T` |
`F` |
`F` |
`T` |

`F` |
`T` |
`F` |
`T` |

`F` |
`F` |
`F` |
`T` |

Whenever expression `A ∧ B`

is `TRUE`

, expression `A | B`

is `FALSE`

, and vice versa. In other words, the first expression is the negation of the second expression. This should bring you straight to the solution for expressing the `AND`

in terms of the `NAND`

:

`(A ∧ B) ⇔ ¬ (A | B)`

If you compare the truth ...

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