Determine the truth value of the statement

~q <-> [ ~r /\ (p \/ q)] 

when p is false, q is true, and r is true. 

Substitute F for p, T for q, and T for r.

You need these truth tables:

~T <=> F
~F <=> T


T \/ T <=> T
T \/ F <=> T
F \/ T <=> T
F \/ F <=> F

T /\ T <=> T
T /\ F <=> F
F /\ T <=> F
F /\ F <=> F

T <-> T <=> T
T <-> F <=> F
F <-> T <=> F
F <-> F <=> T


Substitute F for p, T for q, and T for r.

~q <-> [~r /\ (p \/ q)]

~T <-> [~T /\ (F \/ T)]

Replace both ~T's by F

F <-> [F /\ (F \/ T)]

Replace (F \/ T) by T

F <-> [F /\ T]

Replace [F /\ T] by F

F <-> F

Replace that by

T

Edwin