Question $12$

The truth$-$functional connective SNERG has the following truth$-$table:

p$....$q$....$r$.....$SNERG$($p$,$q$,$r$)$

T$....$T$.....$T$....$F

T$....$T$.....$F$.....$F

T$....$F$.....$T$.....$F

T$.....$F$.....$F$....$T

F$.....$T$....$T$.....$T

F$.....$T$.....$F$....$F

F$....$F$....$T$.....$F

F$.....$F$....$F$.....$F

Which of the following would be true if and only if SNERG $($p$,$q$.$r$)$ is true?

a$)q$ and $r$ are both true but $p$ is false

b$)$ Either $q$ is true or else it is the case that $p$ is false and $r$ is false

c$)$ Either $p$ is false while $q$ and $r$ are true, or else $p$ is true while $q$ and $r$ are false

d$)$ Either $r$ is false, or else $q$ is false and $p$ is true.