Question

$2$

: Logic and Computational Complexity Note: For parts

$($

a

$)$

$-$

$($

d

$)$

$$we assume a fixed propositional language built from the propositional variables

$\{$

$$

$,$

$$

$,$

$$

$\}$

$.$

$($

a

$)$

$$Suppose the value assigned to

$$

$$is

$$

$,$

$$the value assigned to

$$

$$is

$$

$,$

$$and the value assigned to

$$

$$is

$$

$.$

$$Give the truth

$-$

values of the following sentences:

$($

i

$)$

$($

$$

notr

$)$

$$

$$

$$

$$

$$