Question

If p is true and ~ q is false, then p ~ q is _____ false.

Answer 1

Given
`\( p \)` as true and
`\( q \)` as false, evaluating
`\( \\eg (p \land q) \)` results in
`\( \text{True} \).` The conjunction
`\( p \land q \)` is false, and its negation yields a true statement.

Given:

`\( p \)` is true.

`\( q \)` is false.

Evaluating the expression
`\( \\eg (p \land q) \),` which means the negation of the conjunction (AND operation) of
`\( p \)` and
`\( q \)`.

Determine
`\( p \land q \)` (the AND operation of
`\( p \)` and
`\( q \)`):

`\( p \land q \)` =
`\( \text{True} \land \text{False} \)`

Since the AND operation
`(\( \land \))` yields true only when both
`\( p \)` and
`\( q \)` are true, and in this case,
`\( q \)` is false, the result is
`\( \text{False} \)` .

Calculate the negation of
`\( p \land q \)` (denoted as
`\( \\eg (p \land q) \))`:

`\( \\eg (p \land q) \)` =
`\( \\eg (\text{False}) \)`

The negation of false is
`\( \text{True} \)`.

Therefore, the solution is
`\( \\eg (p \land q)` =
`\text{True} \)`, which means the expression is true when
`\( p \)` is true and
`\( q \)` is false.

complete the Question:

If
`\( p \)` is true and
`\( q \)` is false, what is the truth value of
`\( \\eg (p \land q) \)`?