Question 124460: Determine the truth value of the statement ~q <-> [ ~ r ^ (p v q)] when p is false, q is true, and r is true.
Answer by Edwin McCravy(20060)   (Show Source):
You can put this solution on YOUR website!
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
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